Finite Group Databasebeta

← Group #10824518

Character table — Group #10824518

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222223444444444444666666612121212121212121212121244444444444412121212121212121212121212121212121212121212121288888888444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ9111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111-1111-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111-1111-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ11111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1
χ12111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111-1-1-11-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-111
χ13111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1111-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ14111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1111-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ15111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-11-1-1-111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ16111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-11-1-1-111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-22200-2-200000022-2-222-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-20022000000-2-222-2-222000000000000000000000000000000000000
χ19222222222-2-2-2-22222-2-2-2-22222222-2-2-2-22222-2-2-2-22-200-2200000022-2-2-2-222000000000000000000000000000000000000
χ20222222222-2-2-2-22222-2-2-2-22222222-2-2-2-22222-2-2-2-2-22002-2000000-2-22222-2-2000000000000000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000000000000000
χ2522222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112200-2-2000000-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2622222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112200-2-2000000-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2722222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-2002200000011-1-111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ2822222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-2-2002200000011-1-111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ2922222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-111112-200-22000000-1-11111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ3022222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-111112-200-22000000-1-11111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ3122222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-11111-22002-200000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3222222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-11111-1-1-1-11111-22002-200000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3322222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-12-2222-222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-11111111100000000000000000000
χ3422222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-12-2-2-22-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-100000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1-2222-22-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-1-22-2-2-222222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ3722-2-22-2-2222i2i−2i−2i2i2i−2i−2i2-22-222-2-2-2-222i2i−2i−2i2i2i−2i−2i22-2-20000002i−2i002-20000000000002i−2i2i−2i00002-22-200000000000000000000
χ3822-2-22-2-2222i2i−2i−2i2i2i−2i−2i2-22-222-2-2-2-222i2i−2i−2i2i2i−2i−2i22-2-2000000−2i2i00-22000000000000−2i2i−2i2i0000-22-2200000000000000000000
χ3922-2-22-2-2222i2i−2i−2i−2i−2i2i2i-22-2222-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-222002i−2i00002-200000000002i−2i2i−2i00002-22-2000000000000000000000000
χ4022-2-22-2-2222i2i−2i−2i−2i−2i2i2i-22-2222-2-2-2-222i2i−2i−2i−2i−2i2i2i-2-22200−2i2i0000-220000000000−2i2i−2i2i0000-22-22000000000000000000000000
χ4122-2-22-2-222−2i−2i2i2i2i2i−2i−2i-22-2222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-222002i−2i0000-2200000000002i−2i2i−2i0000-22-22000000000000000000000000
χ4222-2-22-2-222−2i−2i2i2i2i2i−2i−2i-22-2222-2-2-2-22−2i−2i2i2i2i2i−2i−2i-2-22200−2i2i00002-20000000000−2i2i−2i2i00002-22-2000000000000000000000000
χ4322-2-22-2-222−2i−2i2i2i−2i−2i2i2i2-22-222-2-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-20000002i−2i00-220000000000002i−2i2i−2i0000-22-2200000000000000000000
χ4422-2-22-2-222−2i−2i2i2i−2i−2i2i2i2-22-222-2-2-2-22−2i−2i2i2i−2i−2i2i2i22-2-2000000−2i2i002-2000000000000−2i2i−2i2i00002-22-200000000000000000000
χ4522-2-22-2-22-12i2i−2i−2i2i2i−2i−2i2-22-2-1-11111-1−i−iii−i−iii-1-1110000002i−2i002-2−i3i3−i3i33−33−33−3−33−ii−ii−i3i3i3−i3-11-1100000000000000000000
χ4622-2-22-2-22-12i2i−2i−2i2i2i−2i−2i2-22-2-1-11111-1−i−iii−i−iii-1-1110000002i−2i002-2i3−i3i3−i3−33−33−333−3−ii−iii3−i3−i3i3-11-1100000000000000000000
χ4722-2-22-2-22-12i2i−2i−2i2i2i−2i−2i2-22-2-1-11111-1−i−iii−i−iii-1-111000000−2i2i00-22−i3i3−i3i33−33−3−333−3i−ii−ii3−i3−i3i31-11-100000000000000000000
χ4822-2-22-2-22-12i2i−2i−2i2i2i−2i−2i2-22-2-1-11111-1−i−iii−i−iii-1-111000000−2i2i00-22i3−i3i3−i3−33−333−3−33i−ii−i−i3i3i3−i31-11-100000000000000000000
χ4922-2-22-2-22-12i2i−2i−2i−2i−2i2i2i-22-22-1-11111-1−i−iiiii−i−i11-1-1002i−2i00002-200−i3i3i3−i33−3−33−ii−ii3−3−33-11-11−i3i3i3−i300000000000000000000
χ5022-2-22-2-22-12i2i−2i−2i−2i−2i2i2i-22-22-1-11111-1−i−iiiii−i−i11-1-1002i−2i00002-200i3−i3−i3i3−333−3−ii−ii−333−3-11-11i3−i3−i3i300000000000000000000
χ5122-2-22-2-22-12i2i−2i−2i−2i−2i2i2i-22-22-1-11111-1−i−iiiii−i−i11-1-100−2i2i0000-2200−i3i3i3−i33−3−33i−ii−i−333−31-11-1i3−i3−i3i300000000000000000000
χ5222-2-22-2-22-12i2i−2i−2i−2i−2i2i2i-22-22-1-11111-1−i−iiiii−i−i11-1-100−2i2i0000-2200i3−i3−i3i3−333−3i−ii−i3−3−331-11-1−i3i3i3−i300000000000000000000
χ5322-2-22-2-22-1−2i−2i2i2i2i2i−2i−2i-22-22-1-11111-1ii−i−i−i−iii11-1-1002i−2i0000-2200−i3i3i3−i3−333−3−ii−ii3−3−331-11-1i3−i3−i3i300000000000000000000
χ5422-2-22-2-22-1−2i−2i2i2i2i2i−2i−2i-22-22-1-11111-1ii−i−i−i−iii11-1-1002i−2i0000-2200i3−i3−i3i33−3−33−ii−ii−333−31-11-1−i3i3i3−i300000000000000000000
χ5522-2-22-2-22-1−2i−2i2i2i2i2i−2i−2i-22-22-1-11111-1ii−i−i−i−iii11-1-100−2i2i00002-200−i3i3i3−i3−333−3i−ii−i−333−3-11-11−i3i3i3−i300000000000000000000
χ5622-2-22-2-22-1−2i−2i2i2i2i2i−2i−2i-22-22-1-11111-1ii−i−i−i−iii11-1-100−2i2i00002-200i3−i3−i3i33−3−33i−ii−i3−3−33-11-11i3−i3−i3i300000000000000000000
χ5722-2-22-2-22-1−2i−2i2i2i−2i−2i2i2i2-22-2-1-11111-1ii−i−iii−i−i-1-1110000002i−2i00-22−i3i3−i3i3−33−333−3−33−ii−iii3−i3−i3i31-11-100000000000000000000
χ5822-2-22-2-22-1−2i−2i2i2i−2i−2i2i2i2-22-2-1-11111-1ii−i−iii−i−i-1-1110000002i−2i00-22i3−i3i3−i33−33−3−333−3−ii−ii−i3i3i3−i31-11-100000000000000000000
χ5922-2-22-2-22-1−2i−2i2i2i−2i−2i2i2i2-22-2-1-11111-1ii−i−iii−i−i-1-111000000−2i2i002-2−i3i3−i3i3−33−33−333−3i−ii−i−i3i3i3−i3-11-1100000000000000000000
χ6022-2-22-2-22-1−2i−2i2i2i−2i−2i2i2i2-22-2-1-11111-1ii−i−iii−i−i-1-111000000−2i2i002-2i3−i3i3−i33−33−33−3−33i−ii−ii3−i3−i3i3-11-1100000000000000000000
χ612-22-2-22-2222i−2i2i−2i2i−2i2i−2i2-2-22-2-222-2-222i−2i2i−2i2i−2i2i−2i2-22-200000000000000000000000000000000000000000000000000002-22i−2i
χ622-22-2-22-2222i−2i2i−2i2i−2i2i−2i2-2-22-2-222-2-222i−2i2i−2i2i−2i2i−2i2-22-20000000000000000000000000000000000000000000000000000-22−2i2i
χ632-22-2-22-2222i−2i2i−2i−2i2i−2i2i-222-2-2-222-2-222i−2i2i−2i−2i2i−2i2i-22-2200000000000000000000000000000000000022-2-22i2i−2i−2i000000000000
χ642-22-2-22-2222i−2i2i−2i−2i2i−2i2i-222-2-2-222-2-222i−2i2i−2i−2i2i−2i2i-22-22000000000000000000000000000000000000-2-222−2i−2i2i2i000000000000
χ652-22-2-22-222−2i2i−2i2i2i−2i2i−2i-222-2-2-222-2-22−2i2i−2i2i2i−2i2i−2i-22-2200000000000000000000000000000000000022-2-2−2i−2i2i2i000000000000
χ662-22-2-22-222−2i2i−2i2i2i−2i2i−2i-222-2-2-222-2-22−2i2i−2i2i2i−2i2i−2i-22-22000000000000000000000000000000000000-2-2222i2i−2i−2i000000000000
χ672-22-2-22-222−2i2i−2i2i−2i2i−2i2i2-2-22-2-222-2-22−2i2i−2i2i−2i2i−2i2i2-22-200000000000000000000000000000000000000000000000000002-2−2i2i
χ682-22-2-22-222−2i2i−2i2i−2i2i−2i2i2-2-22-2-222-2-22−2i2i−2i2i−2i2i−2i2i2-22-20000000000000000000000000000000000000000000000000000-222i−2i
χ692-2-22-2-22222-2-222-2-2222-2-2-2-2-2-22222-2-222-2-222-2-22000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ702-2-22-2-22222-2-222-2-2222-2-2-2-2-2-22222-2-222-2-222-2-2200000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ712-2-22-2-22222-2-22-222-2-2-222-2-2-2-22222-2-22-222-2-222-20000000000000000000000000000000000000000000000002-22-20000
χ722-2-22-2-22222-2-22-222-2-2-222-2-2-2-22222-2-22-222-2-222-2000000000000000000000000000000000000000000000000-22-220000
χ732-2-22-2-2222-222-22-2-22-2-222-2-2-2-2222-222-22-2-22-222-20000000000000000000000000000000000000000000000002-2-220000
χ742-2-22-2-2222-222-22-2-22-2-222-2-2-2-2222-222-22-2-22-222-2000000000000000000000000000000000000000000000000-222-20000
χ752-2-22-2-2222-222-2-222-222-2-2-2-2-2-2222-222-2-222-22-2-22000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ762-2-22-2-2222-222-2-222-222-2-2-2-2-2-2222-222-2-222-22-2-2200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ77444-4-4-44-440000000000004-44-44-4-400000000000000000000000000000000000000000000000022−2222−220000000000000000
χ78444-4-4-44-440000000000004-44-44-4-4000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ7944-44-44-4-440000000000004-4-44-44-4000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ8044-44-44-4-440000000000004-4-44-44-40000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ814-4444-4-4-44000000000000-444-4-44-400000000000000000000000000000000000000000000000022−22−22220000000000000000
χ824-4444-4-4-44000000000000-444-4-44-4000000000000000000000000000000000000000000000000−222222−220000000000000000
χ834-44-4-44-44-24i−4i4i−4i4i−4i4i−4i4-4-4422-2-222-2−2i2i−2i2i−2i2i−2i2i-22-2200000000000000000000000000000000000000000000000000000000
χ844-44-4-44-44-24i−4i4i−4i−4i4i−4i4i-444-422-2-222-2−2i2i−2i2i2i−2i2i−2i2-22-200000000000000000000000000000000000000000000000000000000
χ854-44-4-44-44-2−4i4i−4i4i4i−4i4i−4i-444-422-2-222-22i−2i2i−2i−2i2i−2i2i2-22-200000000000000000000000000000000000000000000000000000000
χ864-44-4-44-44-2−4i4i−4i4i−4i4i−4i4i4-4-4422-2-222-22i−2i2i−2i2i−2i2i−2i-22-2200000000000000000000000000000000000000000000000000000000
χ874-4-44-4-444-24-4-444-4-4444-4-42222-2-2-2-222-2-222-2-222-200000000000000000000000000000000000000000000000000000000
χ884-4-44-4-444-24-4-44-444-4-4-4442222-2-2-2-222-22-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ894-4-44-4-444-2-444-44-4-44-4-4442222-2-2-22-2-22-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ904-4-44-4-444-2-444-4-444-444-4-42222-2-2-22-2-222-2-22-222-200000000000000000000000000000000000000000000000000000000
χ914-4-4-4444-44000000000000-44-444-4-40000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ924-4-4-4444-44000000000000-44-444-4-400000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ93888-8-8-88-8-4000000000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ9488-88-88-8-8-4000000000000-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ958-8888-8-8-8-40000000000004-4-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-8888-8-40000000000004-44-4-44400000000000000000000000000000000000000000000000000000000000000000000

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