Finite Group Databasebeta

← Group #10691992

Character table — Group #10691992

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order12222234444446661212121244466121212121212888888881212242424242424242424242424242424248824242424444488882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111
χ411111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ51111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ91111-1-111-11-1-1-1111111111-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i1-111-1-11-11-1ii−i−i1-1i−i
χ101111-1-111-11-1-1-1111111111-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11iiii−i−i−i−iiiii−i−i−i−i1-111-1-1-11-11−i−iii-11−ii
χ111111-1-111-11-1-1-1111111111-1-1-1-1-1-1-1-1-1ii−i−i−i−iii11−i−i−i−iiiiiiiii−i−i−i−i-11-1-1111-11-1−i−iii-11i−i
χ121111-1-111-11-1-1-1111111111-1-1-1-1-1-1-1-1-1ii−i−i−i−iii11−i−i−i−iiiiiiiii−i−i−i−i-11-1-111-11-11ii−i−i1-1−ii
χ131111-1-111-11-1-1-1111111111-1-1-1-1-1-1-1-1-1−i−iiiii−i−i11iiii−i−i−i−i−i−i−i−iiiii-11-1-1111-11-1ii−i−i-11−ii
χ141111-1-111-11-1-1-1111111111-1-1-1-1-1-1-1-1-1−i−iiiii−i−i11iiii−i−i−i−i−i−i−i−iiiii-11-1-111-11-11−i−iii1-1i−i
χ151111-1-111-11-1-1-1111111111-1-1-1-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii1-111-1-11-11-1−i−iii1-1−ii
χ161111-1-111-11-1-1-1111111111-1-1-1-1-1-1-1-1-1−i−iii−i−iii11−i−i−i−iiiii−i−i−i−iiiii1-111-1-1-11-11ii−i−i-11i−i
χ1722222222222-2-22222222-2-2-2222-2-2-2-2200000000-2-2000000000000000000000022-2-200000000
χ1822222222222-2-22222222-2-2-2222-2-2-2-2200000000-2-20000000000000000000000-2-22200000000
χ192222222-2-2-2-222222-2-2-2-22-2-222-2-2-222-200002-22-22-222-2-222-2-200000000000000000000000000
χ202222222-2-2-2-222222-2-2-2-22-2-222-2-2-222-20000-22-222-2-2-222-2-22200000000000000000000000000
χ212222222-2-2-2-2-2-2222-2-2-2-2-22222-222-2-2-200000000-22000000000000000000000000002i−2i2i−2i0000
χ222222222-2-2-2-2-2-2222-2-2-2-2-22222-222-2-2-200000000-2200000000000000000000000000−2i2i−2i2i0000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ25222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ26222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-1000000000000
χ27222222-1-2-2-2-222-1-1-111112-2-2-1-1111-1-1100002-22-2-11-1-111-1-11133−3−333−3−3003−33−3000000000000
χ28222222-1-2-2-2-222-1-1-111112-2-2-1-1111-1-1100002-22-2-11-1-111-1-111−3−333−3−33300−33−33000000000000
χ29222222-1-2-2-2-222-1-1-111112-2-2-1-1111-1-110000-22-22-1111-1-111-1-133−3−333−3−300−33−33000000000000
χ30222222-1-2-2-2-222-1-1-111112-2-2-1-1111-1-110000-22-22-1111-1-111-1-1−3−333−3−333003−33−3000000000000
χ312222-2-222-22-2222222222-2-22-2-2-22222-200000000-2-200000000000000000000002-2-2200000000
χ322222-2-222-22-2222222222-2-22-2-2-22222-200000000-2-20000000000000000000000-222-200000000
χ332222-2-22-22-2222222-2-2-2-2-22-2-2-22-2-222200000000-22000000000000000000000000002-2-220000
χ342222-2-22-22-2222222-2-2-2-2-22-2-2-22-2-222200000000-2200000000000000000000000000-222-20000
χ352222-2-22-22-22-2-2222-2-2-2-22-22-2-2222-2-2200002i−2i−2i2i2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ362222-2-22-22-22-2-2222-2-2-2-22-22-2-2222-2-220000−2i2i2i−2i2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ372222-2-2-12-22-2-2-2-1-1-1-1-1-1-122-2111111112i2i−2i−2i2i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii2-2-1-111000000000000
χ382222-2-2-12-22-2-2-2-1-1-1-1-1-1-122-2111111112i2i−2i−2i−2i−2i2i2i-1-1iiii−i−i−i−i−i−i−i−iiiii-2211-1-1000000000000
χ392222-2-2-12-22-2-2-2-1-1-1-1-1-1-122-211111111−2i−2i2i2i2i2i−2i−2i-1-1−i−i−i−iiiiiiiii−i−i−i−i-2211-1-1000000000000
χ402222-2-2-12-22-2-2-2-1-1-1-1-1-1-122-211111111−2i−2i2i2i−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i2-2-1-111000000000000
χ412222-2-2-1-22-22-2-2-1-1-111112-2211-1-1-111-100002i−2i−2i2i-11−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300−333−3000000000000
χ422222-2-2-1-22-22-2-2-1-1-111112-2211-1-1-111-100002i−2i−2i2i-11−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i3003−3−33000000000000
χ432222-2-2-1-22-22-2-2-1-1-111112-2211-1-1-111-10000−2i2i2i−2i-11ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i3003−3−33000000000000
χ442222-2-2-1-22-22-2-2-1-1-111112-2211-1-1-111-10000−2i2i2i−2i-11ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300−333−3000000000000
χ45444444-24444-4-4-2-2-2-2-2-2-2-4-4-4-2-2-22222-200000000220000000000000000000000000000000000
χ46444444-2-4-4-4-4-4-4-2-2-22222-444-2-22-2-2222000000002-20000000000000000000000000000000000
χ474444-4-4-24-44-444-2-2-2-2-2-2-2-4-44222-2-2-2-2200000000220000000000000000000000000000000000
χ484444-4-4-2-44-4444-2-2-22222-44-422-222-2-2-2000000002-20000000000000000000000000000000000
χ494-44-400400004i−4i4-4-40000000000004i−4i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ504-44-400400004i−4i4-4-40000000000004i−4i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ514-44-40040000−4i4i4-4-4000000000000−4i4i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ524-44-40040000−4i4i4-4-4000000000000−4i4i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ534-44-400-200004i−4i-22223−2323−23000000−2i32i3−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23000000000000000000
χ544-44-400-200004i−4i-22223−2323−23000000−2i32i3−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23000000000000000000
χ554-44-400-200004i−4i-222−2323−23230000002i3−2i3−2i2i02ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23000000000000000000
χ564-44-400-200004i−4i-222−2323−23230000002i3−2i3−2i2i0−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23000000000000000000
χ574-44-400-20000−4i4i-22223−2323−230000002i3−2i32i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23000000000000000000
χ584-44-400-20000−4i4i-22223−2323−230000002i3−2i32i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23000000000000000000
χ594-44-400-20000−4i4i-222−2323−2323000000−2i32i32i−2i0−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23000000000000000000
χ604-44-400-20000−4i4i-222−2323−2323000000−2i32i32i−2i02ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23000000000000000000
χ614-4-444-4444-4-400-44-444-4-40004-440000-400000000000000000000000000000000000000000000
χ624-4-444-44-4-44400-44-4-4-4440004-4-40000400000000000000000000000000000000000000000000
χ634-4-444-4-244-4-4002-22-2-222000-22-2000020000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000000
χ644-4-444-4-244-4-4002-22-2-222000-22-2000020000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000000
χ654-4-444-4-2-4-444002-2222-2-2000-2220000-20000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000
χ664-4-444-4-2-4-444002-2222-2-2000-2220000-20000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000
χ674-4-44-4444-4-4400-44-444-4-4000-44-40000400000000000000000000000000000000000000000000
χ684-4-44-444-444-400-44-4-4-444000-4440000-400000000000000000000000000000000000000000000
χ694-4-44-44-24-4-44002-22-2-2220002-220000-200000000006−66−6−66−6600000000000000000000000000
χ704-4-44-44-24-4-44002-22-2-2220002-220000-20000000000−66−666−66−600000000000000000000000000
χ714-4-44-44-2-444-4002-2222-2-20002-2-20000200000000006−6−66−666−600000000000000000000000000
χ724-4-44-44-2-444-4002-2222-2-20002-2-2000020000000000−666−66−6−6600000000000000000000000000
χ7388-8-8008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ7488-8-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000
χ7588-8-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000

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