Finite Group Databasebeta

← Group #10693564

Character table — Group #10693564

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122222223444444446666666121212121212121244888888881212121212121212242424242424242424242424242424248888888824242424242424242424242424242424444488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91-111-1-1-1111-11-1-11-11-1-1-1-111111-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−iii−i−i11-1-1i−i1-1
χ101-111-1-1-1111-11-1-11-11-1-1-1-111111-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i−i−iii-1-111−ii-11
χ111-111-1-1-1111-11-1-11-11-1-1-1-111111-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiiiii−i−i11-1-1−ii-11
χ121-111-1-1-1111-11-1-11-11-1-1-1-111111-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii−i−iii-1-111i−i1-1
χ131-111-1-1-1111-11-1-11-11-1-1-1-111111-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiiiii−i−i-1-111i−i-11
χ141-111-1-1-1111-11-1-11-11-1-1-1-111111-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii−i−iii11-1-1−ii1-1
χ151-111-1-1-1111-11-1-11-11-1-1-1-111111-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−iii−i−i-1-111−ii1-1
χ161-111-1-1-1111-11-1-11-11-1-1-1-111111-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i−i−iii11-1-1i−i-11
χ1722222222222-2-2-222-2222222222222222-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000002-22-200000000
χ1822222222222-2-2-222-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-22-2200000000
χ19222222222-2-2222-2-222222222-2-2-2-2-2-2-2-2-2-222-2-222-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ20222222222-2-2222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-22222-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ22222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-22222-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ2722222222-1-2-2222-2-22-1-1-1-1-1-1-111111111-2-222-2-222-2-2-1-11111-1-1-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−3000000000000
χ2822222222-1-2-2222-2-22-1-1-1-1-1-1-111111111-2-222-2-222-2-2-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−333000000000000
χ2922222222-1-2-2222-2-22-1-1-1-1-1-1-111111111-2-2-2-222-2-222-1-11111-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−333000000000000
χ3022222222-1-2-2222-2-22-1-1-1-1-1-1-111111111-2-2-2-222-2-222-1-11111-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−3000000000000
χ3122-2-2-2-22220022-200-222-2-22-2-20000000000002-2002-22-200002-2000022-2-2000022-2-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3222-2-2-2-22220022-200-222-2-22-2-20000000000002-2002-22-200002-2000022-2-2000022-2-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3322-2-2-2-22220022-200-222-2-22-2-2000000000000-2200-222-200002-20000-2-2220000-2-222−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3422-2-2-2-22220022-200-222-2-22-2-2000000000000-2200-222-200002-20000-2-2220000-2-222i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3522-2-2-2-222-10022-200-2-1-111-1113−33−33−33−300002-2002-2-113−33−3-1133−3−3-1-11133−3−3-1-111−i2i2−i2i2−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ3622-2-2-2-222-10022-200-2-1-111-1113−33−33−33−300002-2002-2-113−33−3-1133−3−3-1-11133−3−3-1-111i2−i2i2−i2i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ3722-2-2-2-222-10022-200-2-1-111-1113−33−33−33−30000-2200-22-113−33−3-11−3−33311-1-1−3−33311-1-1−i2i2−i2i2i2−i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ3822-2-2-2-222-10022-200-2-1-111-1113−33−33−33−30000-2200-22-113−33−3-11−3−33311-1-1−3−33311-1-1i2−i2i2−i2−i2i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ3922-2-2-2-222-10022-200-2-1-111-111−33−33−33−3300002-2002-2-11−33−33-11−3−333-1-111−3−333-1-111−i2i2−i2i2−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ4022-2-2-2-222-10022-200-2-1-111-111−33−33−33−3300002-2002-2-11−33−33-11−3−333-1-111−3−333-1-111i2−i2i2−i2i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ4122-2-2-2-222-10022-200-2-1-111-111−33−33−33−330000-2200-22-11−33−33-1133−3−311-1-133−3−311-1-1−i2i2−i2i2i2−i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ4222-2-2-2-222-10022-200-2-1-111-111−33−33−33−330000-2200-22-11−33−33-1133−3−311-1-133−3−311-1-1i2−i2i2−i2−i2i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ432-222-2-2-2222-2-2222-2-2-2-2-2-222222-2-222-2-2-2200000000-2-2-2-2222200000000000000000000000000000000000000002i−2i−2i2i00000000
χ442-222-2-2-2222-2-2222-2-2-2-2-2-222222-2-222-2-2-2200000000-2-2-2-222220000000000000000000000000000000000000000−2i2i2i−2i00000000
χ452-222-2-2-222-222-2-2-222-2-2-2-2222-2-222-2-222-222i2i−2i−2i−2i−2i2i2i22-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ462-222-2-2-222-222-2-2-222-2-2-2-2222-2-222-2-222-22−2i−2i2i2i2i2i−2i−2i22-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ472-222-2-2-222-22-222-22-2-2-2-2-2222-2-222-2-2222-200000000-2-222-2-222000000000000000000000000000000000000000000002i−2i−2i2i0000
χ482-222-2-2-222-22-222-22-2-2-2-2-2222-2-222-2-2222-200000000-2-222-2-22200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ492-222-2-2-22-12-22-2-22-221111-1-1-1-1-111-1-1112-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii000000000000
χ502-222-2-2-22-12-22-2-22-221111-1-1-1-1-111-1-1112-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i000000000000
χ512-222-2-2-22-12-22-2-22-221111-1-1-1-1-111-1-1112-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i000000000000
χ522-222-2-2-22-12-22-2-22-221111-1-1-1-1-111-1-1112-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii000000000000
χ532-222-2-2-22-1-222-2-2-2221111-1-1-111-1-111-1-1-222i2i−2i−2i−2i−2i2i2i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i0000000033−3−3−3−333i3i3−i3−i3−i3−i3i3i3000000000000
χ542-222-2-2-22-1-222-2-2-2221111-1-1-111-1-111-1-1-222i2i−2i−2i−2i−2i2i2i-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000−3−33333−3−3−i3−i3i3i3i3i3−i3−i3000000000000
χ552-222-2-2-22-1-222-2-2-2221111-1-1-111-1-111-1-1-22−2i−2i2i2i2i2i−2i−2i-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii0000000033−3−3−3−333−i3−i3i3i3i3i3−i3−i3000000000000
χ562-222-2-2-22-1-222-2-2-2221111-1-1-111-1-111-1-1-22−2i−2i2i2i2i2i−2i−2i-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00000000−3−33333−3−3i3i3−i3−i3−i3−i3i3i3000000000000
χ572-2-2-222-222002-2200-2-2-2222-2-20000000000002i−2i00−2i2i2-20000-2200002i2i−2i−2i0000−2i−2i2i2i−i2i2i2−i22−2−22−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ582-2-2-222-222002-2200-2-2-2222-2-20000000000002i−2i00−2i2i2-20000-2200002i2i−2i−2i0000−2i−2i2i2ii2−i2−i2i2−222−2i2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ592-2-2-222-222002-2200-2-2-2222-2-2000000000000−2i2i002i−2i2-20000-220000−2i−2i2i2i00002i2i−2i−2i−i2i2i2−i2−222−2−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ602-2-2-222-222002-2200-2-2-2222-2-2000000000000−2i2i002i−2i2-20000-220000−2i−2i2i2i00002i2i−2i−2ii2−i2−i2i22−2−22i2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ612-2-2-222-22-1002-2200-211-1-1-1113−3−333−3−3300002i−2i00−2i2i-113−3−331-1i3i3−i3−i3−i−iii−i3−i3i3i3ii−i−i−i2i2i2−i22−2−22ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ622-2-2-222-22-1002-2200-211-1-1-1113−3−333−3−3300002i−2i00−2i2i-113−3−331-1i3i3−i3−i3−i−iii−i3−i3i3i3ii−i−ii2−i2−i2i2−222−2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ632-2-2-222-22-1002-2200-211-1-1-1113−3−333−3−330000−2i2i002i−2i-113−3−331-1−i3−i3i3i3ii−i−ii3i3−i3−i3−i−iii−i2i2i2−i2−222−2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000000000
χ642-2-2-222-22-1002-2200-211-1-1-1113−3−333−3−330000−2i2i002i−2i-113−3−331-1−i3−i3i3i3ii−i−ii3i3−i3−i3−i−iiii2−i2−i2i22−2−22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000000000
χ652-2-2-222-22-1002-2200-211-1-1-111−333−3−333−300002i−2i00−2i2i-11−333−31-1−i3−i3i3i3−i−iiii3i3−i3−i3ii−i−i−i2i2i2−i22−2−22ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000000000
χ662-2-2-222-22-1002-2200-211-1-1-111−333−3−333−300002i−2i00−2i2i-11−333−31-1−i3−i3i3i3−i−iiii3i3−i3−i3ii−i−ii2−i2−i2i2−222−2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
χ672-2-2-222-22-1002-2200-211-1-1-111−333−3−333−30000−2i2i002i−2i-11−333−31-1i3i3−i3−i3ii−i−i−i3−i3i3i3−i−iii−i2i2i2−i2−222−2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000000000
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χ994-4-444-44-4-2-4-40004402-2-2222-22222-2-2-2-2000000000000000000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6000000000000000000000000000000000000
χ1004-4-4-444-44400-44-4004-4-4444-4-4000000000000000000-4400004-40000000000000000000000000000000000000000000000000000
χ1014-4-4-444-44-200-44-400422-2-2-22223−23−232323−23−232300000000002-2−232323−23-220000000000000000000000000000000000000000000000000000
χ1024-4-4-444-44-200-44-400422-2-2-222−232323−23−232323−2300000000002-223−23−2323-220000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.