Finite Group Databasebeta

← Group #13161956

Character table — Group #13161956

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222222244444444444444444444444444444444448888888888888888888888888888888888363636363636363636363636363636363636727272727272727272
order1222233366666233333466666666666666666666666661212666666666666666666666612121212121212121212121222444466661212121212121212444121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111-111111-1111111-1-111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-111-1-11111-11-1-1-111-1-1
χ61111111111111-111111-1111111-1-111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-111-1-1-1-1-1-11-1111-1-111
χ71111111111111-111111-1111111-1-111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1111111-1-11-1-1-1-111
χ81111111111111-111111-1111111-1-111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111-1-1-1-111-11111-1-1
χ92222222-12222-122-1-1-1-12222-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222200-1-1-1-1-1-1-1-10000000000000
χ102222222-12222-122-1-1-1-12222-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200111111110000000000000
χ112222222-12222-1-22-1-1-1-1-2222-1-1-11122-1-1-1-1-1-1-1-12-1-1-1-12211-2-222-1-1-1-1-1-1-1-1-2-211111111-2-2-2-2111111112-22-200-1-111-1-1110000000000000
χ122222222-12222-1-22-1-1-1-1-2222-1-1-11122-1-1-1-1-1-1-1-12-1-1-1-12211-2-222-1-1-1-1-1-1-1-1-2-211111111-2-2-2-211111111-22-220011-1-111-1-10000000000000
χ13222222-122-1-1-122-12-1-1-122-1-122222-1-122-1-1-1-1-1-1-12-1-1-122222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-100002200000000-1-1-1-1200-1-10000
χ14222222-122-1-1-122-12-1-1-122-1-122222-1-122-1-1-1-1-1-1-12-1-1-122222-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-10000-2-2000000001111-200110000
χ15222222-122-1-1-12-2-12-1-1-1-22-1-1222-2-2-1-122-1-1-1-1-1-1-12-1-1-122-2-2-21-1-122-1-1-1-1-1-111-2-2111111-2111-2-211111100002200000000-1-1-1-1-200110000
χ16222222-122-1-1-12-2-12-1-1-1-22-1-1222-2-2-1-122-1-1-1-1-1-1-12-1-1-122-2-2-21-1-122-1-1-1-1-1-111-2-2111111-2111-2-21111110000-2-2000000001111200-1-10000
χ1722222-122-122222-1-12-1-12-12222222-1-1-1-122-1-1-1-1-1-12-1-1-1-122-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-100000000000000000002200-1-1-1-1
χ1822222-122-122222-1-12-1-12-12222222-1-1-1-122-1-1-1-1-1-12-1-1-1-122-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-10000000000000000000-2-2001111
χ1922222-122-12222-2-1-12-1-1-2-122222-2-2-1-1-1-122-1-1-1-1-1-12-1-1-1-1-2-21-2-1-1-1-122-1-1-1-11111-2-211111-21111-2-2111100000000000000000002-200-1-111
χ2022222-122-12222-2-1-12-1-1-2-122222-2-2-1-1-1-122-1-1-1-1-1-12-1-1-1-1-2-21-2-1-1-1-122-1-1-1-11111-2-211111-21111-2-211110000000000000000000-220011-1-1
χ21222-2-222222222222222-22-2-22-2-222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000
χ22222-2-222222222-22222222-2-22-2-2-2-2222222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222000000000000000000000000000
χ23222-2-222-12222-122-1-1-1-1-22-2-2-111-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-21122-2-21111111122-1-1-1-1-1-1-1-1-2-2-2-211111111000000−i3i3−i3i3−i3i3−i3i30000000000000
χ24222-2-222-12222-122-1-1-1-1-22-2-2-111-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-21122-2-21111111122-1-1-1-1-1-1-1-1-2-2-2-211111111000000i3−i3i3−i3i3−i3i3−i30000000000000
χ25222-2-222-12222-1-22-1-1-1-122-2-2-1111122-1-1-1-1-1-1-1-12-1-1-1-1-2-2-1-1-2-2-2-211111111-2-2111111112222-1-1-1-1-1-1-1-1000000−i3i3i3−i3−i3i3i3−i30000000000000
χ26222-2-222-12222-1-22-1-1-1-122-2-2-1111122-1-1-1-1-1-1-1-12-1-1-1-1-2-2-1-1-2-2-2-211111111-2-2111111112222-1-1-1-1-1-1-1-1000000i3−i3−i3i3i3−i3−i3i30000000000000
χ27222-2-22-122-1-1-122-12-1-1-1-22112-2-222-1-122-1-1-1-1-1-1-12-1-1-1-2-2-2-22-111-2-2111111-1-122-1-1-1-1-1-1-2111-2-211111100000000000000−i3−i3i3i3000−i3i30000
χ28222-2-22-122-1-1-122-12-1-1-1-22112-2-222-1-122-1-1-1-1-1-1-12-1-1-1-2-2-2-22-111-2-2111111-1-122-1-1-1-1-1-1-2111-2-211111100000000000000i3i3−i3−i3000i3−i30000
χ29222-2-22-122-1-1-12-2-12-1-1-122112-2-2-2-2-1-122-1-1-1-1-1-1-12-1-1-1-2-222-2111-2-211111111-2-21111112-1-1-122-1-1-1-1-1-100000000000000−i3−i3i3i3000i3−i30000
χ30222-2-22-122-1-1-12-2-12-1-1-122112-2-2-2-2-1-122-1-1-1-1-1-1-12-1-1-1-2-222-2111-2-211111111-2-21111112-1-1-122-1-1-1-1-1-100000000000000i3i3−i3−i3000−i3i30000
χ31222-2-2-122-122222-1-12-1-1-2-1-2-22-2-222-1-1-1-122-1-1-1-1-1-12-1-111-2-2-121111-2-21111-1-1-1-122-1-1-1-11-21111-2-21111000000000000000000000003−33−3
χ32222-2-2-122-122222-1-12-1-1-2-1-2-22-2-222-1-1-1-122-1-1-1-1-1-12-1-111-2-2-121111-2-21111-1-1-1-122-1-1-1-11-21111-2-2111100000000000000000000000−33−33
χ33222-2-2-122-12222-2-1-12-1-12-1-2-22-2-2-2-2-1-1-1-122-1-1-1-1-1-12-1-111221-21111-2-211111111-2-21111-12-1-1-1-122-1-1-1-1000000000000000000000003−3−33
χ34222-2-2-122-12222-2-1-12-1-12-1-2-22-2-2-2-2-1-1-1-122-1-1-1-1-1-12-1-111221-21111-2-211111111-2-21111-12-1-1-1-122-1-1-1-100000000000000000000000−333−3
χ3522-22-22222-2-2220222220-22-2-22-200-2-2-2-2-2-2-2-2-2-2222222-200002-22-22-222-2-20000000000000000000000020-200002200-2-20000000000000
χ3622-22-22222-2-2220222220-22-2-22-200-2-2-2-2-2-2-2-2-2-2222222-200002-22-22-222-2-200000000000000000000000-2020000-2-200220000000000000
χ3722-22-222-12-2-22-102-1-1-1-10-22-21-11−i3i3-2-2111111112-1-1-1-12-2−i3i3002-2-11-11-1-11100−i3i3−i3i3−i3−i3i3i30000−i3i3−i3i3−i3−i3i3i3020-200−i3i3-1-1i3−i3110000000000000
χ3822-22-222-12-2-22-102-1-1-1-10-22-21-11−i3i3-2-2111111112-1-1-1-12-2−i3i3002-2-11-11-1-11100−i3i3−i3i3−i3−i3i3i30000−i3i3−i3i3−i3−i3i3i30-20200i3−i311−i3i3-1-10000000000000
χ3922-22-222-12-2-22-102-1-1-1-10-22-21-11i3−i3-2-2111111112-1-1-1-12-2i3−i3002-2-11-11-1-11100i3−i3i3−i3i3i3−i3−i30000i3−i3i3−i3i3i3−i3−i3020-200i3−i3-1-1−i3i3110000000000000
χ4022-22-222-12-2-22-102-1-1-1-10-22-21-11i3−i3-2-2111111112-1-1-1-12-2i3−i3002-2-11-11-1-11100i3−i3i3−i3i3i3−i3−i30000i3−i3i3−i3i3i3−i3−i30-20200−i3i311i3−i3-1-10000000000000
χ4122-2-222222-2-2220222220-2-22-2-2200-2-2-2-2-2-2-2-2-2-222222-220000-22-22-22-2-222000000000000000000000020-20002200-2-2000000000000000
χ4222-2-222222-2-2220222220-2-22-2-2200-2-2-2-2-2-2-2-2-2-222222-220000-22-22-22-2-2220000000000000000000000-202000-2-20022000000000000000
χ4322-2-2222-12-2-22-102-1-1-1-10-2-2211-1−i3i3-2-2111111112-1-1-1-1-22i3−i300-221-11-111-1-100−i3i3−i3i3−i3−i3i3i30000i3−i3i3−i3i3i3−i3−i320-2000-1-1−i3i311i3−i30000000000000
χ4422-2-2222-12-2-22-102-1-1-1-10-2-2211-1−i3i3-2-2111111112-1-1-1-1-22i3−i300-221-11-111-1-100−i3i3−i3i3−i3−i3i3i30000i3−i3i3−i3i3i3−i3−i3-20200011i3−i3-1-1−i3i30000000000000
χ4522-2-2222-12-2-22-102-1-1-1-10-2-2211-1i3−i3-2-2111111112-1-1-1-1-22−i3i300-221-11-111-1-100i3−i3i3−i3i3i3−i3−i30000−i3i3−i3i3−i3−i3i3i320-2000-1-1i3−i311−i3i30000000000000
χ4622-2-2222-12-2-22-102-1-1-1-10-2-2211-1i3−i3-2-2111111112-1-1-1-1-22−i3i300-221-11-111-1-100i3−i3i3−i3i3i3−i3−i30000−i3i3−i3i3−i3−i3i3i3-20200011−i3i3-1-1i3−i30000000000000
χ47444444-2-24-2-2-2-24-2-211144-2-2-2-2-2-2-2-2-2-2-2111111-2-211144-2-24-2-2-2-2-2111111-2-2-2-21111114-2-2-2-2-2111111000000000000000000000000000
χ48444444-2-24-2-2-2-2-4-2-2111-44-2-2-2-2-222-2-2-2-2111111-2-21114422-42-2-2-2-21111112222-1-1-1-1-1-1-422222-1-1-1-1-1-1000000000000000000000000000
χ4944444-24-2-2444-24-21-2114-244-2-2-2-2-2-2-211-2-21111-21-211-2-2-2-2-24-2-211-2-21111-2-211-2-21111-24-2-211-2-21111000000000000000000000000000
χ5044444-24-2-2444-2-4-21-211-4-244-2-2-222-2-211-2-21111-21-211-2-2222-4-2-211-2-2111122-1-122-1-1-1-12-422-1-122-1-1-1-1000000000000000000000000000
χ5144444-2-24-2-2-2-2441-2-2114-2-2-24444411-2-2-2-211111-2-211-2-244-2-211-2-2-2-2111111-2-2-2-21111-2-211-2-2-2-21111000000000000000000000000000
χ5244444-2-24-2-2-2-24-41-2-211-4-2-2-2444-4-411-2-2-2-211111-2-211-2-2-4-42211-2-2-2-21111-1-12222-1-1-1-122-1-12222-1-1-1-1000000000000000000000000000
χ5344444-2-2-2-2-2-2-2-24111−1−3i32−1+3i324-2-2-2-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000
χ5444444-2-2-2-2-2-2-2-24111−1+3i32−1−3i324-2-2-2-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000
χ5544444-2-2-2-2-2-2-2-2-4111−1−3i32−1+3i32-4-2-2-2-2-2-222111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-22222111111−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000
χ5644444-2-2-2-2-2-2-2-2-4111−1+3i32−1−3i32-4-2-2-2-2-2-222111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-22222111111−1+3i32−1−3i32−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000
χ57444-4-44-2-24-2-2-2-24-2-2111-4422-222-2-2-2-2-2-2111111-2-2111-4-4224-22222-1-1-1-1-1-1-2-2-2-2111111-422222-1-1-1-1-1-1000000000000000000000000000
χ58444-4-44-2-24-2-2-2-2-4-2-21114422-22222-2-2-2-2111111-2-2111-4-4-2-2-422222-1-1-1-1-1-12222-1-1-1-1-1-14-2-2-2-2-2111111000000000000000000000000000
χ59444-4-4-24-2-2444-24-21-211-4-2-4-4-222-2-2-2-211-2-21111-21-2112222-2422-1-122-1-1-1-1-2-211-2-211112-422-1-122-1-1-1-1000000000000000000000000000
χ60444-4-4-24-2-2444-2-4-21-2114-2-4-4-22222-2-211-2-21111-21-21122-2-22-422-1-122-1-1-1-122-1-122-1-1-1-1-24-2-211-2-21111000000000000000000000000000
χ61444-4-4-2-24-2-2-2-2441-2-211-4-2224-4-44411-2-2-2-211111-2-21122-4-4-2-2-1-12222-1-1-1-111-2-2-2-2111122-1-12222-1-1-1-1000000000000000000000000000
χ62444-4-4-2-24-2-2-2-24-41-2-2114-2224-4-4-4-411-2-2-2-211111-2-211224422-1-12222-1-1-1-1-1-12222-1-1-1-1-2-211-2-2-2-21111000000000000000000000000000
χ63444-4-4-2-2-2-2-2-2-2-24111−1−3i32−1+3i32-4-222-222-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i322222-2-2-1-1-1-1-1-11+3i321−3i321+3i321−3i32111111−1−3i32−1+3i32−1−3i32−1+3i3222-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000
χ64444-4-4-2-2-2-2-2-2-2-24111−1+3i32−1−3i32-4-222-222-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i322222-2-2-1-1-1-1-1-11−3i321+3i321−3i321+3i32111111−1+3i32−1−3i32−1+3i32−1−3i3222-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000
χ65444-4-4-2-2-2-2-2-2-2-2-4111−1−3i32−1+3i324-222-22222111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i3222-2-222-1-1-1-1-1-11+3i321−3i321+3i321−3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000
χ66444-4-4-2-2-2-2-2-2-2-2-4111−1+3i32−1−3i324-222-22222111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i3222-2-222-1-1-1-1-1-11−3i321+3i321−3i321+3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000
χ6744-44-44-24422-240-24-2-2-20-4-22-44-40022-4-4222222-24-2-2-24-40000-224-4-22-2-2220000000000000000000000000000000000000000000000000
χ6844-44-44-2-2422-2-20-2-21110-4-222-22−2i32i32222-1-1-1-1-1-1-2-21114-4−2i32i300-22-221-111-1-100−2i32i3i3−i3i3i3−i3−i30000−2i32i3i3−i3i3i3−i3−i3000000000000000000000000000
χ6944-44-44-2-2422-2-20-2-21110-4-222-222i3−2i32222-1-1-1-1-1-1-2-21114-42i3−2i300-22-221-111-1-1002i3−2i3−i3i3−i3−i3i3i300002i3−2i3−i3i3−i3−i3i3i3000000000000000000000000000
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χ914-4000444-400-4-40444440000000000000000000-4-4-4-4-40000000000000000000000000000000000000000002i−2i000000002i−2i2i−2i000000000
χ924-4000444-400-4-40444440000000000000000000-4-4-4-4-4000000000000000000000000000000000000000000−2i2i00000000−2i2i−2i2i000000000
χ934-40004-24-4−2i32i32-40-24-2-2-2000000000−2i32i300−2i32i3−2i32i3−2i32i32-42220000000000000000000000000000000000000000002i−2i000000002ζ7−2ζ72ζ11−2ζ11000000000
χ944-40004-24-4−2i32i32-40-24-2-2-2000000000−2i32i300−2i32i3−2i32i3−2i32i32-4222000000000000000000000000000000000000000000−2i2i00000000−2ζ72ζ7−2ζ112ζ11000000000
χ954-40004-24-42i3−2i32-40-24-2-2-20000000002i3−2i3002i3−2i32i3−2i32i3−2i32-42220000000000000000000000000000000000000000002i−2i000000002ζ11−2ζ112ζ7−2ζ7000000000
χ964-40004-24-42i3−2i32-40-24-2-2-20000000002i3−2i3002i3−2i32i3−2i32i3−2i32-4222000000000000000000000000000000000000000000−2i2i00000000−2ζ112ζ11−2ζ72ζ7000000000
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χ988-80008-4-4-8−4i34i3440-4-4222000000000−4i34i3002i3−2i32i3−2i32i3−2i344-2-2-200000000000000000000000000000000000000000000000000000000000000000
χ998-80008-4-4-84i3−4i3440-4-42220000000004i3−4i300−2i32i3−2i32i3−2i32i344-2-2-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8000-488400-8-80-4-48-4-4000000000000000000044-84400000000000000000000000000000000000000000000000000000000000000000
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χ1028-8000-48-4400-840-42-42200000000000-6600-666-64-24-2-200000000000000000000000000000000000000000000000000000000000000000
χ1038-8000-4-484−4i34i34-802-4-4220000000002i3−2i300−4i34i32i3−2i32i3−2i3-244-2-200000000000000000000000000000000000000000000000000000000000000000
χ1048-8000-4-4844i3−4i34-802-4-422000000000−2i32i3004i3−4i3−2i32i3−2i32i3-244-2-200000000000000000000000000000000000000000000000000000000000000000
χ1058-8000-4-4-44−4i34i3440222−1−3i3−1+3i30000000002i3−2i36-62i3−2i3−3−i33+i33−i3−3+i3-2-2-21+3i31−3i300000000000000000000000000000000000000000000000000000000000000000
χ1068-8000-4-4-44−4i34i3440222−1+3i3−1−3i30000000002i3−2i3-662i3−2i33−i3−3+i3−3−i33+i3-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000000
χ1078-8000-4-4-444i3−4i3440222−1−3i3−1+3i3000000000−2i32i3-66−2i32i33+i3−3−i3−3+i33−i3-2-2-21+3i31−3i300000000000000000000000000000000000000000000000000000000000000000
χ1088-8000-4-4-444i3−4i3440222−1+3i3−1−3i3000000000−2i32i36-6−2i32i3−3+i33−i33+i3−3−i3-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.