Finite Group Databasebeta

← Group #10691282

Character table — Group #10691282

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122244442234444446661212121244661212121212122444444466121212121212121212121212121212128888888888242424248888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-11-11-1ii−i−i111-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−iii−i−iii−i−i11-1-11-1
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-11-11-1ii−i−i111-111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiii−iii−i−i−i−iii-1-111-11
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-11-11-1−i−iii111-111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−ii−i−iiiii−i−i-1-111-11
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-11-11-1−i−iii111-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−i−iii−i−iii11-1-11-1
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1-11-11ii−i−i-1-11-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−i−iii−i−iii11-1-1-11
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1-11-11ii−i−i-1-11-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−ii−i−iiiii−i−i-1-1111-1
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1-11-11−i−iii-1-11-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−iii−i−i−i−iii-1-1111-1
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1-11-11−i−iii-1-11-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−iii−i−iii−i−i11-1-1-11
χ17222222222222-2-22-2-22222222-2-22222-2-2-2-222-2-2000022-2-2-2-222-2-200000000000000000000000000000000
χ18222222222222-2-22-2-22222222-2-22222-2-2-2-2-2-2220000-2-2-2-222-2-22200000000000000000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2222211-1-1111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211-1-1111111111111110000000022-1-1-1-10000000000
χ232222222222-12-2-22-2-2-1-1-1-1-1-1-1-2-2-1-1-1-1111122-2-20000-1-11111-1-111−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ242222222222-12-2-22-2-2-1-1-1-1-1-1-1-2-2-1-1-1-1111122-2-20000-1-11111-1-111i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ252222222222-12-2-22-2-2-1-1-1-1-1-1-1-2-2-1-1-1-11111-2-22200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ262222222222-12-2-22-2-2-1-1-1-1-1-1-1-2-2-1-1-1-11111-2-22200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ2722222222-2-22-222-2222222222-2-2-2-2-2-222220000000000-2-20000000000000022-2-222-2-20000000000000000
χ2822222222-2-22-222-2222222222-2-2-2-2-2-222220000000000-2-200000000000000-2-222-2-2220000000000000000
χ2922222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000002200000000000000000000000000002i−2i2i−2i000000
χ3022222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000000220000000000000000000000000000−2i2i−2i2i000000
χ312222-2-2-2-2222-222-2-2-2222-2-2-2-2-2222-2-222-2-20000000000-22000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2222-222-2-2-2222-2-2-2-2-2222-2-222-2-20000000000-2200000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-2-2-22200000000002-200000000000000000000000000002-2-22000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-2-2-22200000000002-20000000000000000000000000000-222-2000000
χ352222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-222-2-2222-2-22000022-22-2-2-2-22200000000000000000000000000000000
χ362222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-222-2-222-222-20000-2-2-222222-2-200000000000000000000000000000000
χ372222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-1-1112-22-22i2i−2i−2i-1-1-11-1-11111−i−i−i−iiiii000000002i−2i−i−iii0000000000
χ382222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-1-1112-22-2−2i−2i2i2i-1-1-11-1-11111iiii−i−i−i−i00000000−2i2iii−i−i0000000000
χ392222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-1-111-22-222i2i−2i−2i11-1111-1-1-1-1−i−i−i−iiiii00000000−2i2iii−i−i0000000000
χ402222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-1-111-22-22−2i−2i2i2i11-1111-1-1-1-1iiii−i−i−i−i000000002i−2i−i−iii0000000000
χ412222-2-2-2-2-2-2-12-2-2222-1-1-11111-2211-1-111-1-12-2-220000-1-11-11111-1-133−3−3−3−33300000000003−3−330000000000
χ422222-2-2-2-2-2-2-12-2-2222-1-1-11111-2211-1-111-1-12-2-220000-1-11-11111-1-1−3−33333−3−30000000000−333−30000000000
χ432222-2-2-2-2-2-2-12-2-2222-1-1-11111-2211-1-111-1-1-222-20000111-1-1-1-1-11133−3−3−3−3330000000000−333−30000000000
χ442222-2-2-2-2-2-2-12-2-2222-1-1-11111-2211-1-111-1-1-222-20000111-1-1-1-1-111−3−33333−3−300000000003−3−330000000000
χ452-22-22i−2i2i−2i00202-202i−2i2-2-22i−2i2i−2i0000002-22i−2i00001+i−1−i1−i−1+i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000−i2i22−200
χ462-22-22i−2i2i−2i00202-202i−2i2-2-22i−2i2i−2i0000002-22i−2i00001+i−1−i1−i−1+i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000i2−i2−2200
χ472-22-22i−2i2i−2i00202-202i−2i2-2-22i−2i2i−2i0000002-22i−2i0000−1−i1+i−1+i1−i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000i2−i2−2200
χ482-22-22i−2i2i−2i00202-202i−2i2-2-22i−2i2i−2i0000002-22i−2i0000−1−i1+i−1+i1−i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000−i2i22−200
χ492-22-2−2i2i−2i2i00202-20−2i2i2-2-2−2i2i−2i2i0000002-2−2i2i00001−i−1+i1+i−1−i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000i2−i22−200
χ502-22-2−2i2i−2i2i00202-20−2i2i2-2-2−2i2i−2i2i0000002-2−2i2i00001−i−1+i1+i−1−i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000−i2i2−2200
χ512-22-2−2i2i−2i2i00202-20−2i2i2-2-2−2i2i−2i2i0000002-2−2i2i0000−1+i1−i−1−i1+i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000−i2i2−2200
χ522-22-2−2i2i−2i2i00202-20−2i2i2-2-2−2i2i−2i2i0000002-2−2i2i0000−1+i1−i−1−i1+i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000i2−i22−200
χ5344444444-4-4-2-444-444-2-2-2-2-2-2-2-4-42222-2-2-2-200000000002200000000000000000000000000000000000000
χ5444444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000000000-2-200000000000000000000000000000000000000
χ554444-4-4-4-444-2-444-4-4-4-2-2-22222-44-2-222-2-22200000000002-200000000000000000000000000000000000000
χ564444-4-4-4-444-2-4-4-4-444-2-2-222224-4-2-22222-2-20000000000-2200000000000000000000000000000000000000
χ5744-4-444-4-44-44-400400-44-444-4-4004-44-4000000000000000000000000000000000000000000000000000000
χ5844-4-444-4-44-4-2-4004002-22-2-22200-22-22000000000000−2i32i30000−2i32i30000000000000000000000000000000000
χ5944-4-444-4-44-4-2-4004002-22-2-22200-22-220000000000002i3−2i300002i3−2i30000000000000000000000000000000000
χ6044-4-444-4-4-444400-400-44-444-4-400-44-44000000000000000000000000000000000000000000000000000000
χ6144-4-444-4-4-44-2400-4002-22-2-222002-22-2000000000000000023−230023−2300000000000000000000000000000000
χ6244-4-444-4-4-44-2400-4002-22-2-222002-22-20000000000000000−232300−232300000000000000000000000000000000
χ6344-4-4-4-4444-44400-400-44-4-4-444004-4-44000000000000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4-2400-4002-2222-2-200-222-2000000000000000023−2300−232300000000000000000000000000000000
χ6544-4-4-4-4444-4-2400-4002-2222-2-200-222-20000000000000000−23230023−2300000000000000000000000000000000
χ6644-4-4-4-444-444-400400-44-4-4-44400-444-4000000000000000000000000000000000000000000000000000000
χ6744-4-4-4-444-44-2-4004002-2222-2-2002-2-22000000000000−2i32i300002i3−2i30000000000000000000000000000000000
χ6844-4-4-4-444-44-2-4004002-2222-2-2002-2-220000000000002i3−2i30000−2i32i30000000000000000000000000000000000
χ694-44-44i−4i4i−4i0040-440−4i4i4-4-44i−4i4i−4i000000-44−4i4i00000000000000000000000000000000000000000000000000
χ704-44-44i−4i4i−4i00-204-404i−4i-222−2i2i−2i2i000000-22−2i2i00002+2i−2−2i2−2i−2+2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ714-44-44i−4i4i−4i00-204-404i−4i-222−2i2i−2i2i000000-22−2i2i0000−2−2i2+2i−2+2i2−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ724-44-44i−4i4i−4i00-20-440−4i4i-222−2i2i−2i2i0000002-22i−2i000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000
χ734-44-44i−4i4i−4i00-20-440−4i4i-222−2i2i−2i2i0000002-22i−2i000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000
χ744-44-4−4i4i−4i4i0040-4404i−4i4-4-4−4i4i−4i4i000000-444i−4i00000000000000000000000000000000000000000000000000
χ754-44-4−4i4i−4i4i00-204-40−4i4i-2222i−2i2i−2i000000-222i−2i00002−2i−2+2i2+2i−2−2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ764-44-4−4i4i−4i4i00-204-40−4i4i-2222i−2i2i−2i000000-222i−2i0000−2+2i2−2i−2−2i2+2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ774-44-4−4i4i−4i4i00-20-4404i−4i-2222i−2i2i−2i0000002-2−2i2i000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000
χ784-44-4−4i4i−4i4i00-20-4404i−4i-2222i−2i2i−2i0000002-2−2i2i000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000
χ794-4-444i−4i−4i4i004000000-4-444i−4i−4i4i0000000000000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000
χ804-4-444i−4i−4i4i004000000-4-444i−4i−4i4i000000000000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000
χ814-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i0000000000000000000000000000000000002+2i−2−2i002−2i−2+2i000000000000000000
χ824-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i000000000000000000000000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000
χ838-8-888i−8i−8i8i00-400000044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ848-8-88−8i8i8i−8i00-400000044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000

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