Finite Group Databasebeta

← Group #10691136

Character table — Group #10691136

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order12222234444446666666444444444441212121212121212121212121212121212121212121212122244444466661212121212121212121212121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-111-1-1-1-1111-1-1-1-111111-1-1ii−i−i-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-11-1i−iii−i−i11-1-11-1ii−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-111-1-1-1-1111-1-1-1-111111-1-1ii−i−i-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-11-1i−iii−i−i11-1-11-1ii−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-111-1-1-1-1111-1-1-1-111111-1-1−i−iii-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-11-1−ii−i−iii11-1-11-1−i−iii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-111-1-1-1-1111-1-1-1-111111-1-1−i−iii-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-11-1−ii−i−iii11-1-11-1−i−iii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-111-1-1-1-1111-1-1-1-1111-1-111ii−i−i-111-1-1iiii−i−i−i−i11-1-1-1-1-1-11111-11i−i−i−iii-1-1111-1ii−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-111-1-1-1-1111-1-1-1-1111-1-111ii−i−i-111-1-1iiii−i−i−i−i11-1-1-1-1-1-11111-11i−i−i−iii-1-1111-1ii−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-111-1-1-1-1111-1-1-1-1111-1-111−i−iii-111-1-1−i−i−i−iiiii11-1-1-1-1-1-11111-11−iiii−i−i-1-1111-1−i−iiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-111-1-1-1-1111-1-1-1-1111-1-111−i−iii-111-1-1−i−i−i−iiiii11-1-1-1-1-1-11111-11−iiii−i−i-1-1111-1−i−iiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222-2-222222222-2-222220000-2222200000000-2-2-2-222222222-2-2000000-2-2-2-2-2-2000000000000000000000000
χ182222222222-2-222222222-2-2-2-2-2-20000-2222200000000-2-2-2-2-2-2-2-2-2-2-2-2220000002222-2-2000000000000000000000000
χ192222222-2-2-222-22222222-2200002222-2-2-2-2-22222222222220000000000-2-200000000-2-2-2-2-2-200000000000000000000
χ202222222-2-2-222-22222222-220000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000002200000000-2-2222200000000000000000000
χ212222222-2-2-2-2-2-222222222-2000000002-2-2-2-200000000-2-2-2-20000000000002-22-2000022000022-2-222-2-2000000000000
χ222222222-2-2-2-2-2-222222222-2000000002-2-2-2-200000000-2-2-2-2000000000000-22-220000220000-2-222-2-222000000000000
χ23222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-1222222-2-2-2-22-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000
χ25222222-1222222-1-1-1-1-1-1-122-2-2-2-222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2-2-21111-1-1-1-1-1-111111111000000000000
χ26222222-1222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-22-1-1-1-111111111-1-1-1-111111111-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-1000000000000
χ27222222-1222-2-22-1-1-1-1-1-1-1-2-222220000-2-1-1-1-1−i3−i3i3i3−i3−i3i3i31111-1-1-1-1-1-1-1-1-2-2000000111111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-1222-2-22-1-1-1-1-1-1-1-2-222220000-2-1-1-1-1i3i3−i3−i3i3i3−i3−i31111-1-1-1-1-1-1-1-1-2-2000000111111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-2-2-20000-2-1-1-1-1−i3−i3i3i3−i3−i3i3i311111111111122000000-1-1-1-111−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3000000000000
χ30222222-1222-2-22-1-1-1-1-1-1-1-2-2-2-2-2-20000-2-1-1-1-1i3i3−i3−i3i3i3−i3−i311111111111122000000-1-1-1-111i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3000000000000
χ31222222-1-2-2-222-2-1-1-1-1-1-1-1-2200002222-21111-1-1-1-1-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i300-2-20000−i3i3−i3i3111111−i3i3i3−i3−i3i3i3−i3000000000000
χ32222222-1-2-2-222-2-1-1-1-1-1-1-1-2200002222-21111-1-1-1-1-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i300-2-20000i3−i3i3−i3111111i3−i3−i3i3i3−i3−i3i3000000000000
χ33222222-1-2-2-222-2-1-1-1-1-1-1-1-220000-2-2-2-2-2111111111111-1-1-1-1−i3−i3i3i3−i3−i3i3i300220000−i3i3−i3i311-1-1-1-1i3−i3−i3i3i3−i3−i3i3000000000000
χ34222222-1-2-2-222-2-1-1-1-1-1-1-1-220000-2-2-2-2-2111111111111-1-1-1-1i3i3−i3−i3i3i3−i3−i300220000i3−i3i3−i311-1-1-1-1−i3i3i3−i3−i3i3i3−i3000000000000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-20000000021111−i3−i3i3i3−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i300002-22-2i3−i3i3−i3-1-1i3−i3i3−i3-1-111-1-111000000000000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-20000000021111−i3−i3i3i3−i3−i3i3i31111i3i3−i3−i3i3i3−i3−i30000-22-22−i3i3−i3i3-1-1i3−i3i3−i311-1-111-1-1000000000000
χ37222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-20000000021111i3i3−i3−i3i3i3−i3−i31111−i3−i3i3i3−i3−i3i3i30000-22-22i3−i3i3−i3-1-1−i3i3−i3i311-1-111-1-1000000000000
χ38222222-1-2-2-2-2-2-2-1-1-1-1-1-1-12-20000000021111i3i3−i3−i3i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i300002-22-2−i3i3−i3i3-1-1−i3i3−i3i3-1-111-1-111000000000000
χ392222-2-222-2-222222-2-2-2-22-2-222-2-20000222-2-200000000-2-2222222-2-2-2-2-22000000-2-222-22000000000000000000000000
χ402222-2-222-2-222222-2-2-2-22-2-2-2-2220000222-2-200000000-2-222-2-2-2-222222-200000022-2-2-22000000000000000000000000
χ412222-2-22-22222-222-2-2-2-222-200000000-2-2-22200000000-2-2220000000000002i−2i−2i2i00002-200002i2i−2i−2i−2i−2i2i2i000000000000
χ422222-2-22-22222-222-2-2-2-222-200000000-2-2-22200000000-2-222000000000000−2i2i2i−2i00002-20000−2i−2i2i2i2i2i−2i−2i000000000000
χ432222-2-22-222-2-2-222-2-2-2-22-2200002i2i−2i−2i2-2-2222i2i2i2i−2i−2i−2i−2i22-2-20000000000−2i2i00000000-22−2i−2i2i2i00000000000000000000
χ442222-2-22-222-2-2-222-2-2-2-22-220000−2i−2i2i2i2-2-222−2i−2i−2i−2i2i2i2i2i22-2-200000000002i−2i00000000-222i2i−2i−2i00000000000000000000
χ452222-2-2-12-2-2222-1-11111-1-2-222-2-200002-1-11133−3−3−3−33311-1-1-1-1-1-11111-2200000011-1-11-13−3−333−33−3−33−33000000000000
χ462222-2-2-12-2-2222-1-11111-1-2-222-2-200002-1-111−3−33333−3−311-1-1-1-1-1-11111-2200000011-1-11-1−333−3−33−333−33−3000000000000
χ472222-2-2-12-2-2222-1-11111-1-2-2-2-22200002-1-11133−3−3−3−33311-1-11111-1-1-1-12-2000000-1-1111-13−3−33−33−333−33−3000000000000
χ482222-2-2-12-2-2222-1-11111-1-2-2-2-22200002-1-111−3−33333−3−311-1-11111-1-1-1-12-2000000-1-1111-1−333−33−33−3−33−33000000000000
χ492222-2-2-12-2-2-2-22-1-11111-12222-2-22i2i−2i−2i-2-1-111−i−i−i−iiiii-1-111-1-1-1-111112-22i−2i2i2i−2i−2i-1-111-11−i−iii−i−i−i−iiiii000000000000
χ502222-2-2-12-2-2-2-22-1-11111-12222-2-2−2i−2i2i2i-2-1-111iiii−i−i−i−i-1-111-1-1-1-111112-2−2i2i−2i−2i2i2i-1-111-11ii−i−iiiii−i−i−i−i000000000000
χ512222-2-2-12-2-2-2-22-1-11111-122-2-2222i2i−2i−2i-2-1-111−i−i−i−iiiii-1-1111111-1-1-1-1-222i−2i−2i−2i2i2i11-1-1-11−i−iiiiiii−i−i−i−i000000000000
χ522222-2-2-12-2-2-2-22-1-11111-122-2-222−2i−2i2i2i-2-1-111iiii−i−i−i−i-1-1111111-1-1-1-1-22−2i2i2i2i−2i−2i11-1-1-11ii−i−i−i−i−i−iiiii000000000000
χ532222-2-2-1-22222-2-1-11111-12-200000000-211-1-133−3−3−3−33311-1-1−i3−i3i3i3i3i3−i3−i300002i−2i−2i2ii3−i3−i3i3-11−333−3−i−iiiii−i−i000000000000
χ542222-2-2-1-22222-2-1-11111-12-200000000-211-1-133−3−3−3−33311-1-1i3i3−i3−i3−i3−i3i3i30000−2i2i2i−2i−i3i3i3−i3-11−333−3ii−i−i−i−iii000000000000
χ552222-2-2-1-22222-2-1-11111-12-200000000-211-1-1−3−33333−3−311-1-1−i3−i3i3i3i3i3−i3−i30000−2i2i2i−2ii3−i3−i3i3-113−3−33ii−i−i−i−iii000000000000
χ562222-2-2-1-22222-2-1-11111-12-200000000-211-1-1−3−33333−3−311-1-1i3i3−i3−i3−i3−i3i3i300002i−2i−2i2i−i3i3i3−i3-113−3−33−i−iiiii−i−i000000000000
χ572222-2-2-1-222-2-2-2-1-11111-1-2200002i2i−2i−2i211-1-1−i−i−i−iiiii-1-111−i3−i3i3i3i3i3−i3−i300−2i2i0000−i3i3i3−i31-1ii−i−i3−3−33−333−3000000000000
χ582222-2-2-1-222-2-2-2-1-11111-1-2200002i2i−2i−2i211-1-1−i−i−i−iiiii-1-111i3i3−i3−i3−i3−i3i3i300−2i2i0000i3−i3−i3i31-1ii−i−i−333−33−3−33000000000000
χ592222-2-2-1-222-2-2-2-1-11111-1-220000−2i−2i2i2i211-1-1iiii−i−i−i−i-1-111−i3−i3i3i3i3i3−i3−i3002i−2i0000−i3i3i3−i31-1−i−iii−333−33−3−33000000000000
χ602222-2-2-1-222-2-2-2-1-11111-1-220000−2i−2i2i2i211-1-1iiii−i−i−i−i-1-111i3i3−i3−i3−i3−i3i3i3002i−2i0000i3−i3−i3i31-1−i−iii3−3−33−333−3000000000000
χ612-2-222-2222-200-22-222-2-2-2002i−2i2i−2i000002-22-20000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000002−22−2−i2i2−i2i20000
χ622-2-222-2222-200-22-222-2-2-2002i−2i2i−2i000002-22-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000−22−22i2−i2i2−i20000
χ632-2-222-2222-200-22-222-2-2-200−2i2i−2i2i000002-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000002−22−2i2−i2i2−i20000
χ642-2-222-2222-200-22-222-2-2-200−2i2i−2i2i000002-22-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−22−22−i2i2−i2i20000
χ652-2-22-2222-2200-22-2-2-222-2002i−2i−2i2i000002-2-220000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000−i2i2i2−i2−222−20000
χ662-2-22-2222-2200-22-2-2-222-2002i−2i−2i2i000002-2-220000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000i2−i2−i2i22−2−220000
χ672-2-22-2222-2200-22-2-2-222-200−2i2i2i−2i000002-2-22000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000−i2i2i2−i22−2−220000
χ682-2-22-2222-2200-22-2-2-222-200−2i2i2i−2i000002-2-22000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000i2−i2−i2i2−222−20000
χ6944-4-40040004i−4i0-440000-40000002+2i−2−2i2−2i−2+2i000002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i004i−4i0000000000000000000000000000000000000000000000
χ7044-4-40040004i−4i0-440000-4000000−2−2i2+2i−2+2i2−2i00000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i004i−4i0000000000000000000000000000000000000000000000
χ7144-4-4004000−4i4i0-440000-40000002−2i−2+2i2+2i−2−2i000002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00−4i4i0000000000000000000000000000000000000000000000
χ7244-4-4004000−4i4i0-440000-4000000−2+2i2−2i−2−2i2+2i00000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00−4i4i0000000000000000000000000000000000000000000000
χ7344-4-400-20004i−4i02-2−2i32i3−2i32i320000002+2i−2−2i2−2i−2+2i00000−2ζ4+2ζ142ζ4−2ζ14−2ζ20+2ζ222ζ20−2ζ22−2ζ4−2ζ142ζ4+2ζ14−2ζ20−2ζ222ζ20+2ζ2223−23−2i2i0000000000000000000000000000000000000000000000
χ7444-4-400-20004i−4i02-2−2i32i3−2i32i32000000−2−2i2+2i−2+2i2−2i000002ζ4−2ζ14−2ζ4+2ζ142ζ20−2ζ22−2ζ20+2ζ222ζ4+2ζ14−2ζ4−2ζ142ζ20+2ζ22−2ζ20−2ζ2223−23−2i2i0000000000000000000000000000000000000000000000
χ7544-4-400-20004i−4i02-22i3−2i32i3−2i320000002+2i−2−2i2−2i−2+2i00000−2ζ20+2ζ222ζ20−2ζ22−2ζ4+2ζ142ζ4−2ζ14−2ζ20−2ζ222ζ20+2ζ22−2ζ4−2ζ142ζ4+2ζ14−2323−2i2i0000000000000000000000000000000000000000000000
χ7644-4-400-20004i−4i02-22i3−2i32i3−2i32000000−2−2i2+2i−2+2i2−2i000002ζ20−2ζ22−2ζ20+2ζ222ζ4−2ζ14−2ζ4+2ζ142ζ20+2ζ22−2ζ20−2ζ222ζ4+2ζ14−2ζ4−2ζ14−2323−2i2i0000000000000000000000000000000000000000000000
χ7744-4-400-2000−4i4i02-2−2i32i3−2i32i320000002−2i−2+2i2+2i−2−2i00000−2ζ4−2ζ142ζ4+2ζ14−2ζ20−2ζ222ζ20+2ζ22−2ζ4+2ζ142ζ4−2ζ14−2ζ20+2ζ222ζ20−2ζ22−23232i−2i0000000000000000000000000000000000000000000000
χ7844-4-400-2000−4i4i02-2−2i32i3−2i32i32000000−2+2i2−2i−2−2i2+2i000002ζ4+2ζ14−2ζ4−2ζ142ζ20+2ζ22−2ζ20−2ζ222ζ4−2ζ14−2ζ4+2ζ142ζ20−2ζ22−2ζ20+2ζ22−23232i−2i0000000000000000000000000000000000000000000000
χ7944-4-400-2000−4i4i02-22i3−2i32i3−2i320000002−2i−2+2i2+2i−2−2i00000−2ζ20−2ζ222ζ20+2ζ22−2ζ4−2ζ142ζ4+2ζ14−2ζ20+2ζ222ζ20−2ζ22−2ζ4+2ζ142ζ4−2ζ1423−232i−2i0000000000000000000000000000000000000000000000
χ8044-4-400-2000−4i4i02-22i3−2i32i3−2i32000000−2+2i2−2i−2−2i2+2i000002ζ20+2ζ22−2ζ20−2ζ222ζ4+2ζ14−2ζ4−2ζ142ζ20−2ζ22−2ζ20+2ζ222ζ4−2ζ14−2ζ4+2ζ1423−232i−2i0000000000000000000000000000000000000000000000
χ814-4-444-44-4-440044-444-4-4-400000000000-44-440000000000000000000000000000000000000000000000000000000000
χ824-4-444-4-244-400-4-22-2-2222004i−4i4i−4i00000-22-22000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000
χ834-4-444-4-244-400-4-22-2-222200−4i4i−4i4i00000-22-220000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000
χ844-4-444-4-2-4-44004-22-2-2222000000000002-22-200000000000023−23−232323−23−232300000000000000000000000000000000000000
χ854-4-444-4-2-4-44004-22-2-2222000000000002-22-2000000000000−232323−23−232323−2300000000000000000000000000000000000000
χ864-4-44-444-44-40044-4-4-444-400000000000-444-40000000000000000000000000000000000000000000000000000000000
χ874-4-44-44-24-4400-4-2222-2-22004i−4i−4i4i00000-222-2000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000
χ884-4-44-44-24-4400-4-2222-2-2200−4i4i4i−4i00000-222-20000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000
χ894-4-44-44-2-44-4004-2222-2-22000000000002-2-2200000000000023−23−2323−232323−2300000000000000000000000000000000000000
χ904-4-44-44-2-44-4004-2222-2-22000000000002-2-22000000000000−232323−2323−23−232300000000000000000000000000000000000000
χ918-88-8008000000-8-8000080000000000000000000000000000000000000000000000000000000000000000000000000
χ928-88-800-400000044−4i34i34i3−4i3-40000000000000000000000000000000000000000000000000000000000000000000000000
χ938-88-800-4000000444i3−4i3−4i34i3-40000000000000000000000000000000000000000000000000000000000000000000000000

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