Finite Group Databasebeta

← Group #10901325

Character table — Group #10901325

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order122222344444466612121212444661212121212122444444466121212121212121212121212121212128824242424244444442488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-11-1-1-1-111
χ61111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11111-1-1
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-1
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-111-1-111
χ91111111-1-111111111111-1-1-11111-1-1-1-11-1-1111-1-111-1-111-1-1-1-11111-1-1-1-11-111-1-11-1-1111-1-11-11-1
χ101111111-1-111111111111-1-1-11111-1-1-1-11-1-1111-1-111-1-111-1-1-1-11111-1-1-1-11-111-1-1-111-1-1-111-11-11
χ111111111-1-111111111111-1-1-11111-1-1-1-11-1-11-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-1111-1-1111-1-1-11-11
χ121111111-1-111111111111-1-1-11111-1-1-1-11-1-11-1-11111-1-111-1-1-1-1-1-1-1-11111-11-1-111-111-1-1-1111-11-1
χ131111111-1-111111111111-1-1-11111-1-1-1-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1111-1-1-1-1111-111-1
χ141111111-1-111111111111-1-1-11111-1-1-1-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-111-11111-1-1-11-1-11
χ151111111-1-111111111111-1-1-11111-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-11-1-1-1-11111-1-11
χ161111111-1-111111111111-1-1-11111-1-1-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-11111-1-1-1-111-1
χ17222222222-2-2-2-2222-2-2-2-22-2-222-2-222-2-200000000002-2000000000000000000000002-202-20000
χ18222222222-2-2-2-2222-2-2-2-22-2-222-2-222-2-200000000002-200000000000000000000000-220-220000
χ192222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-2220000000000-22000000000000000000000002-20-220000
χ202222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-2220000000000-2200000000000000000000000-2202-20000
χ21222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-21111000000000000
χ23222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2222211-1-1111111-1-1-1-1-1-1-1-1-2-21111000000000000
χ24222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211-1-11111111111111122-1-1-1-1000000000000
χ25222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-1-1-1-111112-2-2222-2-2-1-111-1-11111-1-1-1-111112-2-1-111000000000000
χ26222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-1-1-1-111112-2-22-2-222-1-111-1-111111111-1-1-1-1-2211-1-1000000000000
χ27222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-222-222-2-2111111-1-1-1-1-1-1-1-11111-2211-1-1000000000000
χ28222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-1-1-1-11111-222-2-2-222111111-1-1-1-11111-1-1-1-12-2-1-111000000000000
χ292222-2-22222-22-22222222-22-2-2-2-2-222220000000000-2-20000000000000000000022-200-2000000
χ302222-2-22222-22-22222222-22-2-2-2-2-222220000000000-2-200000000000000000000-2-22002000000
χ312222-2-2222-22-22222-2-2-2-2-2-22-2-22222-2-222-2-2000022-22-2-222-2-200000000000000000000000000
χ322222-2-2222-22-22222-2-2-2-2-2-22-2-22222-2-2-2-2220000-2-2-2222-2-22200000000000000000000000000
χ332222-2-22-2-22-22-222222222-22-2-2-2-2-2-2-2-2000000000022000000000000000000002-2200-2000000
χ342222-2-22-2-22-22-222222222-22-2-2-2-2-2-2-2-200000000002200000000000000000000-22-2002000000
χ352222-2-22-2-2-22-22222-2-2-2-222-2-2-222-2-2222-22-20000222-2-2-2-2-22200000000000000000000000000
χ362222-2-22-2-2-22-22222-2-2-2-222-2-2-222-2-222-22-220000-2-22-22222-2-200000000000000000000000000
χ372222-2-2-122-22-22-1-1-11111-2-2211-1-1-1-11122-2-20000-1-11-111-1-11133−3−333−3−3003−33−3000000000000
χ382222-2-2-122-22-22-1-1-11111-2-2211-1-1-1-11122-2-20000-1-11-111-1-111−3−333−3−33300−33−33000000000000
χ392222-2-2-122-22-22-1-1-11111-2-2211-1-1-1-111-2-2220000111-1-1-111-1-133−3−333−3−300−33−33000000000000
χ402222-2-2-122-22-22-1-1-11111-2-2211-1-1-1-111-2-2220000111-1-1-111-1-1−3−333−3−333003−33−3000000000000
χ412222-2-2-1-2-2-22-22-1-1-1111122-211-1-111-1-12-22-20000-1-1-111111-1-133−3−3−3−333003−3−33000000000000
χ422222-2-2-1-2-2-22-22-1-1-1111122-211-1-111-1-12-22-20000-1-1-111111-1-1−3−33333−3−300−333−3000000000000
χ432222-2-2-1-2-2-22-22-1-1-1111122-211-1-111-1-1-22-22000011-11-1-1-1-11133−3−3−3−33300−333−3000000000000
χ442222-2-2-1-2-2-22-22-1-1-1111122-211-1-111-1-1-22-22000011-11-1-1-1-111−3−33333−3−3003−3−33000000000000
χ45444444-244-4-4-4-4-2-2-222224-4-4-2-222-2-2220000000000-2200000000000000000000000000000000
χ46444444-2-4-4-4-4-4-4-2-2-22222-444-2-22222-2-200000000002-200000000000000000000000000000000
χ474444-4-4-2444-44-4-2-2-2-2-2-2-2-44-42222-2-2-2-200000000002200000000000000000000000000000000
χ484444-4-4-2-4-44-44-4-2-2-2-2-2-2-24-44222222220000000000-2-200000000000000000000000000000000
χ494-44-40044i−4i00004-4-4000000000004i−4i0000002-22i−2i00000000002-22-22i−2i2i−2i000000000000000000
χ504-44-40044i−4i00004-4-4000000000004i−4i000000-22−2i2i0000000000-22-22−2i2i−2i2i000000000000000000
χ514-44-4004−4i4i00004-4-400000000000−4i4i0000002-2−2i2i00000000002-22-2−2i2i−2i2i000000000000000000
χ524-44-4004−4i4i00004-4-400000000000−4i4i000000-222i−2i0000000000-22-222i−2i2i−2i000000000000000000
χ534-44-400-24i−4i0000-22223−2323−230000000−2i2i−2i32i300002-22i−2i0000000000−1+31−3−1−31+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000
χ544-44-400-24i−4i0000-22223−2323−230000000−2i2i−2i32i30000-22−2i2i00000000001−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000
χ554-44-400-24i−4i0000-222−2323−23230000000−2i2i2i3−2i300002-22i−2i0000000000−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000
χ564-44-400-24i−4i0000-222−2323−23230000000−2i2i2i3−2i30000-22−2i2i00000000001+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000
χ574-44-400-2−4i4i0000-22223−2323−2300000002i−2i2i3−2i300002-2−2i2i0000000000−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000
χ584-44-400-2−4i4i0000-22223−2323−2300000002i−2i2i3−2i30000-222i−2i00000000001−3−1+31+3−1−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000
χ594-44-400-2−4i4i0000-222−2323−232300000002i−2i−2i32i300002-2−2i2i0000000000−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000
χ604-44-400-2−4i4i0000-222−2323−232300000002i−2i−2i32i30000-222i−2i00000000001+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000
χ614-4-444-440044-4-4-44-444-4-40004-44-4000000000000000000000000000000000000000000000000
χ624-4-444-4400-4-444-44-4-4-4440004-4-44000000000000000000000000000000000000000000000000
χ634-4-444-4-20044-4-42-22-2-222000-22-22000000000000−2i32i300−2i32i3000000000000000000000000000000
χ644-4-444-4-20044-4-42-22-2-222000-22-220000000000002i3−2i3002i3−2i3000000000000000000000000000000
χ654-4-444-4-200-4-4442-2222-2-2000-222-200000000000000000023−2323−2300000000000000000000000000
χ664-4-444-4-200-4-4442-2222-2-2000-222-2000000000000000000−2323−232300000000000000000000000000
χ674-4-44-444004-4-44-44-444-4-4000-44-44000000000000000000000000000000000000000000000000
χ684-4-44-44400-444-4-44-4-4-444000-444-4000000000000000000000000000000000000000000000000
χ694-4-44-44-2004-4-442-22-2-2220002-22-200000000000000000023−23−232300000000000000000000000000
χ704-4-44-44-2004-4-442-22-2-2220002-22-2000000000000000000−232323−2300000000000000000000000000
χ714-4-44-44-200-444-42-2222-2-20002-2-22000000000000−2i32i3002i3−2i3000000000000000000000000000000
χ724-4-44-44-200-444-42-2222-2-20002-2-220000000000002i3−2i300−2i32i3000000000000000000000000000000
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 12 (ζ12 = 1); i = ζ3.