Finite Group Databasebeta

← Group #72226163

Character table — Group #72226163

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222444444444444444444444444448888888888881616161616161616161616161616161616161616161624242424242424242424242432323232323248484848484848484848
order1222223444466644446688888888121212122424242424242424224412121212242424246688121216161616242424244848484848484848224488888888441212121222228816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ81111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ91-1-111-11-1-111-1-1111-1-11-111-111-1-1-1-1-1111111-1-1-1-11-11-111-1-11-11-11-11-11-1ii−i−i11-1-1iiii−i−i−i−i1-11-1iiii−i−i−i−ii−iii−i−i11-1-11-1ii−i−i
χ101-1-111-11-1-111-1-1111-1-11-111-111-1-1-1-1-1111111-1-1-1-11-11-111-1-11-11-11-11-11-1ii−i−i11-1-1iiii−i−i−i−i-11-11−i−i−i−iiiiii−iii−i−i-1-111-11−i−iii
χ111-1-111-11-1-111-1-1111-1-11-111-111-1-1-1-1-1111111-1-1-1-11-11-111-1-11-11-11-11-11-1−i−iii11-1-1−i−i−i−iiiii1-11-1−i−i−i−iiiii−ii−i−iii11-1-11-1−i−iii
χ121-1-111-11-1-111-1-1111-1-11-111-111-1-1-1-1-1111111-1-1-1-11-11-111-1-11-11-11-11-11-1−i−iii11-1-1−i−i−i−iiiii-11-11iiii−i−i−i−i−ii−i−iii-1-111-11ii−i−i
χ131-1-111-11-1-111-1-1111-1-11-111-111-1-1-1-1-1111111-1-1-1-1-11-1111-1-11-11-1-11-11-11ii−i−i-1-111iiii−i−i−i−i1-11-1iiii−i−i−i−i−ii−i−iii-1-1111-1−i−iii
χ141-1-111-11-1-111-1-1111-1-11-111-111-1-1-1-1-1111111-1-1-1-1-11-1111-1-11-11-1-11-11-11ii−i−i-1-111iiii−i−i−i−i-11-11−i−i−i−iiiii−ii−i−iii11-1-1-11ii−i−i
χ151-1-111-11-1-111-1-1111-1-11-111-111-1-1-1-1-1111111-1-1-1-1-11-1111-1-11-11-1-11-11-11−i−iii-1-111−i−i−i−iiiii1-11-1−i−i−i−iiiiii−iii−i−i-1-1111-1ii−i−i
χ161-1-111-11-1-111-1-1111-1-11-111-111-1-1-1-1-1111111-1-1-1-1-11-1111-1-11-11-1-11-11-11−i−iii-1-111−i−i−i−iiiii-11-11iiii−i−i−i−ii−iii−i−i11-1-1-11−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200002222-2-2-2-200000000000000000000000000000000000000002-22-2000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200002222-2-2-2-20000000000000000000000000000000000000000-22-22000000
χ1922222222222222-2-2-2-222222-2-2-2-222222-2-22222-2-20000-2-2-2-2-2-22200000000000000000000002222000000000000000000-2-20000
χ2022222222222222-2-2-2-222222-2-2-2-222222-2-22222-2-20000-2-2-2-2-2-2220000000000000000000000-2-2-2-2000000000000000000220000
χ2122222222222222-2-2-2-222-2-2-22222-2222222-2-2-2-2222222-2-2-2-222-2-222-2-2220000-2-2-2-2000000000000000000000000000000000000
χ2222222222222222-2-2-2-222-2-2-22222-2222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-222-2-200002222000000000000000000000000000000000000
χ23222222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ24222222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-111111111000000000000-2-211110000000000
χ25222222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-111-2-21122221111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ26222222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-111-2-211-2-2-2-211111111111100000000000022-1-1-1-10000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-2-2-22222-2-1-1-1-1-1-11111-1-122221111-1-111-1-1-2-2-1-100001111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-2-2-22222-2-1-1-1-1-1-11111-1-122221111-1-111-1-1-2-2-1-100001111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ29222222-12222-1-1-1-2-2-2-2-1-1-2-2-22222-2-1-1-1-1-1-11111-1-1-2-2-2-21111-1-1111122110000-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ30222222-12222-1-1-1-2-2-2-2-1-1-2-2-22222-2-1-1-1-1-1-11111-1-1-2-2-2-21111-1-1111122110000-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ312222-2-222-22-22220000-2-22-220000-22-2-22002222000000000000-2-2000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i222-2-2−i2−i2i2i2−i2−i2i2i20000000000000000
χ322222-2-222-22-22220000-2-22-220000-22-2-22002222000000000000-2-2000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2-2-222i2i2−i2−i2i2i2−i2−i20000000000000000
χ332222-2-222-22-22220000-2-22-220000-22-2-22002222000000000000-2-2000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i222-2-2i2i2−i2−i2i2i2−i2−i20000000000000000
χ342222-2-222-22-22220000-2-22-220000-22-2-22002222000000000000-2-2000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2-2-222−i2−i2i2i2−i2−i2i2i20000000000000000
χ352222-2-22-22-222220000-2-20002-22-20-222-2-2-20000-2-222-2-2000022002200-2-200000000000000000000−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i2
χ362222-2-22-22-222220000-2-20002-22-20-222-2-2-20000-2-222-2-2000022002200-2-200000000000000000000i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i2
χ372222-2-22-22-222220000-2-20002-22-20-222-2-2-20000-2-2-2-22200002200-2-2002200000000000000000000−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i2
χ382222-2-22-22-222220000-2-20002-22-20-222-2-2-20000-2-2-2-22200002200-2-2002200000000000000000000i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i2
χ392-2-222-22-2-222-2-2222-2-22-2-2-22-2-2222-2-222-2-2-2-22222000022-2-2-22-2200000000000000000000000000000000000000002-2-22000000
χ402-2-222-22-2-222-2-2222-2-22-2-2-22-2-2222-2-222-2-2-2-22222000022-2-2-22-220000000000000000000000000000000000000000-222-2000000
χ412-2-222-22-2-222-2-22-2-2222-222-2-2-222-2-2-222-2-222-2-2220000-2-222-222-200000000000000000000002-22-2000000000000000000-220000
χ422-2-222-22-2-222-2-22-2-2222-222-2-2-222-2-2-222-2-222-2-2220000-2-222-222-20000000000000000000000-22-220000000000000000002-20000
χ432-2-222-22-2-222-2-22-2-2222-2-2-2222-2-22-2-22222-2-222-2-22-22-2-2-2222-2-222-2-222-20000-2-222000000000000000000000000000000000000
χ442-2-222-22-2-222-2-22-2-2222-2-2-2222-2-22-2-22222-2-222-2-2-22-22-2-2222-2-22-222-2-22000022-2-2000000000000000000000000000000000000
χ452-2-222-2-1-2-22211-122-2-2-1122-222-2-2-211-1-1-1-1-1-111112-22-2-1-111-11-11-112-2-112i2i−2i−2i-1-111−i−i−i−iiiii0000000000002i−2i−i−iii0000000000
χ462-2-222-2-1-2-22211-122-2-2-1122-222-2-2-211-1-1-1-1-1-111112-22-2-1-111-11-11-112-2-11−2i−2i2i2i-1-111iiii−i−i−i−i000000000000−2i2iii−i−i0000000000
χ472-2-222-2-1-2-22211-122-2-2-1122-222-2-2-211-1-1-1-1-1-11111-22-22-1-111-11-111-1-221-12i2i−2i−2i11-1-1−i−i−i−iiiii000000000000−2i2iii−i−i0000000000
χ482-2-222-2-1-2-22211-122-2-2-1122-222-2-2-211-1-1-1-1-1-11111-22-22-1-111-11-111-1-221-1−2i−2i2i2i11-1-1iiii−i−i−i−i0000000000002i−2i−i−iii0000000000
χ492-2-222-2-1-2-22211-1-2-222-11-2-2222-2-2211-1-1-1-111-1-1112-22-211-1-1-111-1-11-22-11000011-1-133−3−3−3−333000000000000003−3−330000000000
χ502-2-222-2-1-2-22211-1-2-222-11-2-2222-2-2211-1-1-1-111-1-1112-22-211-1-1-111-1-11-22-11000011-1-1−3−33333−3−300000000000000−333−30000000000
χ512-2-222-2-1-2-22211-1-2-222-11-2-2222-2-2211-1-1-1-111-1-111-22-2211-1-1-111-11-12-21-10000-1-11133−3−3−3−33300000000000000−333−30000000000
χ522-2-222-2-1-2-22211-1-2-222-11-2-2222-2-2211-1-1-1-111-1-111-22-2211-1-1-111-11-12-21-10000-1-111−3−33333−3−3000000000000003−3−330000000000
χ532-2-22-2222-2-22-2-220000-220002-2-2202-22-2-2-20000222-2-2200002-2002-200-22000000000000000000002−22−2−22−220000000000002−2−22
χ542-2-22-2222-2-22-2-220000-220002-2-2202-22-2-2-20000222-2-2200002-2002-200-2200000000000000000000−22−222−22−2000000000000−222−2
χ552-2-22-2222-2-22-2-220000-220002-2-2202-22-2-2-2000022-222-200002-200-22002-2000000000000000000002−22−2−22−22000000000000−222−2
χ562-2-22-2222-2-22-2-220000-220002-2-2202-22-2-2-2000022-222-200002-200-22002-200000000000000000000−22−222−22−20000000000002−2−22
χ572-2-22-222-222-2-2-220000-222-2-200002-22-220022-2-2000000000000-220000002−2−2200002−22−2−22−222-2-2222−2−2−2−2220000000000000000
χ582-2-22-222-222-2-2-220000-222-2-200002-22-220022-2-2000000000000-220000002−2−2200002−22−2−22−22-222-2−2−22222−2−20000000000000000
χ592-2-22-222-222-2-2-220000-222-2-200002-22-220022-2-2000000000000-22000000−222−20000−22−222−22−22-2-22−2−22222−2−20000000000000000
χ602-2-22-222-222-2-2-220000-222-2-200002-22-220022-2-2000000000000-22000000−222−20000−22−222−22−2-222-222−2−2−2−2220000000000000000
χ614444444-4-4-4-444400004400000000-4-4-4-400000000000000000000000000000000000000000000002-2-222-2-220000000000000000
χ624444444-4-4-4-444400004400000000-4-4-4-40000000000000000000000000000000000000000000000-222-2-222-20000000000000000
χ63444444-24444-2-2-24444-2-2-4-4-4-4-4-4-4-4-2-2-2-2222222220000-2-2-2-2222200000000000000000000000000000000000000000000000000
χ64444444-24444-2-2-2-4-4-4-4-2-2444-4-4-4-44-2-2-2-222-2-2-2-2220000222222-2-200000000000000000000000000000000000000000000000000
χ654444-4-444-44-44440000-4-4-44-4000044-4-4400-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ664444-4-44-44-444440000-4-4000-44-440-444-44400004400000000-4-40000000000000000000000000000000000000000000000000000
χ674444-4-4-24-44-4-2-2-20000224-440000-4-222-200-2-2-2-200000000000022000000−2i22i2−2i22i20000i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ684444-4-4-24-44-4-2-2-20000224-440000-4-222-200-2-2-2-2000000000000220000002i2−2i22i2−2i20000−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ694444-4-4-24-44-4-2-2-2000022-44-400004-222-2002222000000000000-2-2000000000000006−6−666−6−660000000000000000000000000000
χ704444-4-4-24-44-4-2-2-2000022-44-400004-222-2002222000000000000-2-200000000000000−666−6−666−60000000000000000000000000000
χ714444-4-4-2-44-44-2-2-20000220004-44-402-2-222200002244-4-40000-2-200-2-2002200000000000000000000000000000000000000000000
χ724444-4-4-2-44-44-2-2-20000220004-44-402-2-2222000022-4-4440000-2-2002200-2-200000000000000000000000000000000000000000000
χ734444-4-4-2-44-44-2-2-2000022000-44-4402-2-22-2-20000-2-2000000002200000000000023−2323−23000000000000000000000000000000000000
χ744444-4-4-2-44-44-2-2-2000022000-44-4402-2-22-2-20000-2-20000000022000000000000−2323−2323000000000000000000000000000000000000
χ754-4-444-4444-4-4-4-4400004-40000000044-4-400000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ764-4-444-4444-4-4-4-4400004-40000000044-4-40000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ774-4-444-4-2-4-44422-244-4-4-22-4-44-4-444422-2-22222-2-2-2-20000-2-2222-22-200000000000000000000000000000000000000000000000000
χ784-4-444-4-2-4-44422-2-4-444-2244-4-4-444-422-2-222-2-222-2-2000022-2-22-2-2200000000000000000000000000000000000000000000000000
χ794-4-44-4444-4-44-4-440000-44000-444-404-44-4440000-4-400000000-440000000000000000000000000000000000000000000000000000
χ804-4-44-444-444-4-4-440000-44-4440000-4-44-4400-4-4440000000000004-400000000000000000000000000000000000000000000000000
χ814-4-44-44-24-4-4422-200002-20004-4-440-22-22220000-2-24-4-440000-2200-22002-200000000000000000000000000000000000000000000
χ824-4-44-44-24-4-4422-200002-20004-4-440-22-22220000-2-2-444-40000-22002-200-2200000000000000000000000000000000000000000000
χ834-4-44-44-24-4-4422-200002-2000-444-40-22-22-2-2000022000000002-200000000000023−23−2323000000000000000000000000000000000000
χ844-4-44-44-24-4-4422-200002-2000-444-40-22-22-2-2000022000000002-2000000000000−232323−23000000000000000000000000000000000000
χ854-4-44-44-2-444-422-200002-24-4-4000042-22-200-2-2220000000000002-200000022−22−22220000−22−222−22−20000000000000000000000000000
χ864-4-44-44-2-444-422-200002-24-4-4000042-22-200-2-2220000000000002-2000000−222222−2200002−22−2−22−220000000000000000000000000000
χ874-4-44-44-2-444-422-200002-2-4440000-42-22-20022-2-2000000000000-2200000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ884-4-44-44-2-444-422-200002-2-4440000-42-22-20022-2-2000000000000-2200000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ89888888-4-8-8-8-8-4-4-40000-4-40000000044440000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-800800008-8-84-44-4000000000000000000000000004-44-4000000000000000000000000000000000000000000000000000000
χ9188-8-800800008-8-8-44-4400000000000000000000000000-44-44000000000000000000000000000000000000000000000000000000
χ9288-8-800-40000-4444-44-40000000000000026−2626−2626−2626−260000-22-22000000000000000000000000000000000000000000000000000000
χ9388-8-800-40000-4444-44-400000000000000−2626−2626−2626−26260000-22-22000000000000000000000000000000000000000000000000000000
χ9488-8-800-40000-444-44-440000000000000026−26−2626−262626−2600002-22-2000000000000000000000000000000000000000000000000000000
χ9588-8-800-40000-444-44-4400000000000000−262626−2626−26−262600002-22-2000000000000000000000000000000000000000000000000000000
χ968-88-80080000-88-84-4-44000000000000000000000000004-4-44000000000000000000000000000000000000000000000000000000
χ978-88-80080000-88-8-444-400000000000000000000000000-444-4000000000000000000000000000000000000000000000000000000
χ988-88-800-400004-444-4-440000000000000026−2626−26−2626−26260000-222-2000000000000000000000000000000000000000000000000000000
χ998-88-800-400004-444-4-4400000000000000−2626−262626−2626−260000-222-2000000000000000000000000000000000000000000000000000000
χ1008-88-800-400004-44-444-40000000000000026−26−262626−26−262600002-2-22000000000000000000000000000000000000000000000000000000
χ1018-88-800-400004-44-444-400000000000000−262626−26−262626−2600002-2-22000000000000000000000000000000000000000000000000000000
χ1028-8-888-8-488-8-844-40000-4400000000-4-4440000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).