Finite Group Databasebeta

← Group #10691310

Character table — Group #10691310

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order1222444434444444466612121212241212121212121212244466688881212121212121224242424242424248888888888242424248888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-11-1-111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-11-1-111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-111-1-1-111ii−i−i111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−iii−i−i11-1-1ii−i−i1-1
χ101111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-111-1-1-111ii−i−i111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiii−iii−i−i-1-111−i−iii-11
χ111111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-111-1-1-111−i−iii111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−ii−i−iii-1-111ii−i−i-11
χ121111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-111-1-1-111−i−iii111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−i−iii11-1-1−i−iii1-1
χ131111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1-111-1-1-1ii−i−i1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−i−iii11-1-1−i−iii-11
χ141111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1-111-1-1-1ii−i−i1-1-11111iiii−i−i−i−i−i−i−i−iiiii−ii−i−iii-1-111ii−i−i1-1
χ151111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1-111-1-1-1−i−iii1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−iii−i−i-1-111−i−iii1-1
χ161111-1-1-1-1111-1-111-1-1111-1-1-1-1-111111-1-1-1-1-1-111-1-1-1−i−iii1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−iii−i−i11-1-1ii−i−i-11
χ1722222222222-2-2-2-2222222222-2-222-2-222-2-20000-2000000-20000000000000022-2-222-2-20000000000000000
χ1822222222222-2-2-2-2222222222-2-222-2-222-2-20000-2000000-200000000000000-2-222-2-2220000000000000000
χ19222222222-2-22222-2-22222222-2-2-2-222-2-2222-2-22-2220000-2-2-222-2-200000000000000000000000000000000
χ20222222222-2-22222-2-22222222-2-2-2-222-2-222-222-2-2-2-20000-222-2-22200000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000020000002000000000000000000000000000000002i−2i2i−2i00
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200002000000200000000000000000000000000000000−2i2i−2i2i00
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1112222-1111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-111-2-2-2-2-1111111111111110000000022-1-1-1-10000000000
χ2722222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-211-1-111-1-12-2-221-1-10000111-1-111−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ2822222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-211-1-111-1-12-2-221-1-10000111-1-111i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-211-1-111-1-1-222-211100001-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-211-1-111-1-1-222-211100001-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ312222-2-2-2-222222-2-2-2-2222-2-2-2-22-222-2-2-2-22200002000000-2000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-222222-2-2-2-2222-2-2-2-22-222-2-2-2-22200002000000-200000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-22-2-222-2-222222-2-2-2-2-22-2-2-2-222220000-20000002000000000000000000000000000000002-2-2200
χ342222-2-2-2-22-2-222-2-222222-2-2-2-2-22-2-2-2-222220000-2000000200000000000000000000000000000000-222-200
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-22-2-2-22222-2-22-22-22220000-2-2-2-2-22200000000000000000000000000000000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-22-2-2-22222-2-2-22-222-2-20000-22222-2-200000000000000000000000000000000
χ372222-2-2-2-2-122-2-222-2-2-1-1-11111-22-1-1-1-1111122-2-21-1-12i2i−2i−2i-1-1-11111−i−i−i−iiiii000000002i−2i−i−iii0000000000
χ382222-2-2-2-2-122-2-222-2-2-1-1-11111-22-1-1-1-1111122-2-21-1-1−2i−2i2i2i-1-1-11111iiii−i−i−i−i00000000−2i2iii−i−i0000000000
χ392222-2-2-2-2-122-2-222-2-2-1-1-11111-22-1-1-1-11111-2-2221112i2i−2i−2i-111-1-1-1-1−i−i−i−iiiii00000000−2i2iii−i−i0000000000
χ402222-2-2-2-2-122-2-222-2-2-1-1-11111-22-1-1-1-11111-2-222111−2i−2i2i2i-111-1-1-1-1iiii−i−i−i−i000000002i−2i−i−iii0000000000
χ412222-2-2-2-2-1-2-2-2-22222-1-1-111112-211-1-1-1-1112-22-2-1-1-1000011111-1-133−3−3−3−33300000000003−3−330000000000
χ422222-2-2-2-2-1-2-2-2-22222-1-1-111112-211-1-1-1-1112-22-2-1-1-1000011111-1-1−3−33333−3−30000000000−333−30000000000
χ432222-2-2-2-2-1-2-2-2-22222-1-1-111112-211-1-1-1-111-22-22-11100001-1-1-1-11133−3−3−3−3330000000000−333−30000000000
χ442222-2-2-2-2-1-2-2-2-22222-1-1-111112-211-1-1-1-111-22-22-11100001-1-1-1-111−3−33333−3−300000000003−3−330000000000
χ4522-2-22i−2i2i−2i22-200002i−2i2-2-22i−2i2i−2i002-2002i−2i0000000001+i−1−i1−i−1+i00000001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000002−2−i2i2000000
χ4622-2-22i−2i2i−2i22-200002i−2i2-2-22i−2i2i−2i002-2002i−2i0000000001+i−1−i1−i−1+i00000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000−22i2−i2000000
χ4722-2-22i−2i2i−2i22-200002i−2i2-2-22i−2i2i−2i002-2002i−2i000000000−1−i1+i−1+i1−i0000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000−22i2−i2000000
χ4822-2-22i−2i2i−2i22-200002i−2i2-2-22i−2i2i−2i002-2002i−2i000000000−1−i1+i−1+i1−i0000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000002−2−i2i2000000
χ4922-2-2−2i2i−2i2i22-20000−2i2i2-2-2−2i2i−2i2i002-200−2i2i0000000001−i−1+i1+i−1−i00000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000002−2i2−i2000000
χ5022-2-2−2i2i−2i2i22-20000−2i2i2-2-2−2i2i−2i2i002-200−2i2i0000000001−i−1+i1+i−1−i00000001−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000−22−i2i2000000
χ5122-2-2−2i2i−2i2i22-20000−2i2i2-2-2−2i2i−2i2i002-200−2i2i000000000−1+i1−i−1−i1+i0000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000−22−i2i2000000
χ5222-2-2−2i2i−2i2i22-20000−2i2i2-2-2−2i2i−2i2i002-200−2i2i000000000−1+i1−i−1−i1+i0000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000002−2i2−i2000000
χ5344444444-244-4-4-4-444-2-2-2-2-2-2-2-4-4-2-222-2-22200002000000200000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244222222220000-2000000-200000000000000000000000000000000000000
χ554444-4-4-4-4-24444-4-4-4-4-2-2-222224-4-2-22222-2-20000-2000000200000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-444-4-444-2-2-22222-442222-2-2-2-200002000000-200000000000000000000000000000000000000
χ5744-4-44i−4i4i−4i4-440000−4i4i4-4-44i−4i4i−4i00-4400−4i4i0000000000000000000000000000000000000000000000000000
χ5844-4-44i−4i4i−4i-24-400004i−4i-222−2i2i−2i2i00-2200−2i2i0000000002+2i−2−2i2−2i−2+2i0000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000000000
χ5944-4-44i−4i4i−4i-24-400004i−4i-222−2i2i−2i2i00-2200−2i2i000000000−2−2i2+2i−2+2i2−2i00000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000000000
χ6044-4-44i−4i4i−4i-2-440000−4i4i-222−2i2i−2i2i002-2002i−2i00000000000000000000−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
χ6144-4-44i−4i4i−4i-2-440000−4i4i-222−2i2i−2i2i002-2002i−2i00000000000000000000ζ4+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
χ6244-4-4−4i4i−4i4i4-4400004i−4i4-4-4−4i4i−4i4i00-44004i−4i0000000000000000000000000000000000000000000000000000
χ6344-4-4−4i4i−4i4i-24-40000−4i4i-2222i−2i2i−2i00-22002i−2i0000000002−2i−2+2i2+2i−2−2i0000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000000000
χ6444-4-4−4i4i−4i4i-24-40000−4i4i-2222i−2i2i−2i00-22002i−2i000000000−2+2i2−2i−2−2i2+2i00000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000000000
χ6544-4-4−4i4i−4i4i-2-4400004i−4i-2222i−2i2i−2i002-200−2i2i00000000000000000000−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
χ6644-4-4−4i4i−4i4i-2-4400004i−4i-2222i−2i2i−2i002-200−2i2i00000000000000000000ζ4−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
χ674-44-44i−4i−4i4i4004i−4i4-400-44-44i−4i−4i4i00004-4004i−4i00000000000000000000000000000000000000000000000000
χ684-44-44i−4i−4i4i400−4i4i-4400-44-44i−4i−4i4i0000-4400−4i4i00000000000000000000000000000000000000000000000000
χ694-44-44i−4i−4i4i-2004i−4i4-4002-22−2i2i2i−2i0000-2200−2i2i00000000000023−2300−2i32i300000000000000000000000000000000
χ704-44-44i−4i−4i4i-2004i−4i4-4002-22−2i2i2i−2i0000-2200−2i2i000000000000−2323002i3−2i300000000000000000000000000000000
χ714-44-44i−4i−4i4i-200−4i4i-44002-22−2i2i2i−2i00002-2002i−2i00000−2i32i3000000023−230000000000000000000000000000000000
χ724-44-44i−4i−4i4i-200−4i4i-44002-22−2i2i2i−2i00002-2002i−2i000002i3−2i30000000−23230000000000000000000000000000000000
χ734-44-4−4i4i4i−4i4004i−4i-4400-44-4−4i4i4i−4i0000-44004i−4i00000000000000000000000000000000000000000000000000
χ744-44-4−4i4i4i−4i400−4i4i4-400-44-4−4i4i4i−4i00004-400−4i4i00000000000000000000000000000000000000000000000000
χ754-44-4−4i4i4i−4i-2004i−4i-44002-222i−2i−2i2i00002-200−2i2i00000−2i32i30000000−23230000000000000000000000000000000000
χ764-44-4−4i4i4i−4i-2004i−4i-44002-222i−2i−2i2i00002-200−2i2i000002i3−2i3000000023−230000000000000000000000000000000000
χ774-44-4−4i4i4i−4i-200−4i4i4-4002-222i−2i−2i2i0000-22002i−2i00000000000023−23002i3−2i300000000000000000000000000000000
χ784-44-4−4i4i4i−4i-200−4i4i4-4002-222i−2i−2i2i0000-22002i−2i000000000000−232300−2i32i300000000000000000000000000000000
χ794-4-4444-4-4400000000-4-4444-4-4000000000000000000000000000000000000−2i22i200−2i22i2000000000000000000
χ804-4-4444-4-4400000000-4-4444-4-40000000000000000000000000000000000002i2−2i2002i2−2i2000000000000000000
χ814-4-44-4-444400000000-4-44-4-44400000000000000000000000000000000000022−2200−2222000000000000000000
χ824-4-44-4-444400000000-4-44-4-444000000000000000000000000000000000000−22220022−22000000000000000000
χ838-8-8888-8-8-40000000044-4-4-444000000000000000000000000000000000000000000000000000000000000
χ848-8-88-8-888-40000000044-444-4-4000000000000000000000000000000000000000000000000000000000000

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