Finite Group Databasebeta

← Group #10693715

Character table — Group #10693715

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12224444223444444666121212124466121212121212444488881212121212121212121224242424242424248888888888242424248888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111ii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−ii−iii−i−ii−ii−i11-1-11-1
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111ii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiii−iii−i−i−ii−ii-1-111-11
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111ii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i−ii−i−iii−ii−ii11-1-1-11
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111ii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−ii−i−iiii−ii−i-1-1111-1
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−ii−i−iiii−ii−i-1-111-11
χ141111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−ii−i−iii−ii−ii11-1-11-1
χ151111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−ii−iii−i−i−ii−ii-1-1111-1
χ161111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiiii−iii−i−ii−ii−i11-1-1-11
χ17222222222222-2-2-2-222222222-2-22222-2-2-2-200000000-2-200000000000000000000000000000022-2-2000000
χ18222222222222-2-2-2-222222222-2-22222-2-2-2-200000000-2-2000000000000000000000000000000-2-222000000
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
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2322222222-2-22-22222-22222222-2-2-2-2-2-2222200000000-2-2000000000000000022-2-222-2-20000000000000000
χ2422222222-2-22-22222-22222222-2-2-2-2-2-2222200000000-2-20000000000000000-2-222-2-2220000000000000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200002i−2i2i−2i22000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000−2i2i−2i2i2200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2722222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100002i−2i2i−2i-1-133−3−333−3−3−i−iii−i−iii0000000000−i3i3−i3i30000000000
χ2822222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100002i−2i2i−2i-1-1−3−333−3−333−i−iii−i−iii0000000000i3−i3i3−i30000000000
χ2922222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122111111110000−2i2i−2i2i-1-133−3−333−3−3ii−i−iii−i−i0000000000i3−i3i3−i30000000000
χ3022222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122111111110000−2i2i−2i2i-1-1−3−333−3−333ii−i−iii−i−i0000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-222-2-2-2222-2-2-2-2-2222-2-2-2-22200000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2222-222-2-2-2222-2-2-2-2-2222-2-2-2-22200000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-2-222-2222-2-2-2-22-222-2-222-2-200002i−2i−2i2i2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ342222-2-2-2-2222-2-2-222-2222-2-2-2-22-222-2-222-2-20000−2i2i2i−2i2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ352222-2-2-2-222-1-2-2-222-2-1-1-111112-2-1-111-1-11100002i−2i−2i2i-11−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i0000000000−333−30000000000
χ362222-2-2-2-222-1-2-2-222-2-1-1-111112-2-1-111-1-11100002i−2i−2i2i-11i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i00000000003−3−330000000000
χ372222-2-2-2-222-1-2-2-222-2-1-1-111112-2-1-111-1-1110000−2i2i2i−2i-11−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii00000000003−3−330000000000
χ382222-2-2-2-222-1-2-2-222-2-1-1-111112-2-1-111-1-1110000−2i2i2i−2i-11i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii0000000000−333−30000000000
χ392222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-22222-2-200000000-220000000000000000000000000000002i−2i−2i2i000000
χ402222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-22222-2-200000000-22000000000000000000000000000000−2i2i2i−2i000000
χ412222-2-2-2-2-2-2-1222-2-22-1-1-111112-211-1-111-1-12i2i−2i−2i22-2-2-11−i−i−i−iiiii-1-1-1-11111000000002i−2i−i−iii0000000000
χ422222-2-2-2-2-2-2-1222-2-22-1-1-111112-211-1-111-1-12i2i−2i−2i-2-222-11−i−i−i−iiiii1111-1-1-1-100000000−2i2iii−i−i0000000000
χ432222-2-2-2-2-2-2-1222-2-22-1-1-111112-211-1-111-1-1−2i−2i2i2i22-2-2-11iiii−i−i−i−i-1-1-1-1111100000000−2i2iii−i−i0000000000
χ442222-2-2-2-2-2-2-1222-2-22-1-1-111112-211-1-111-1-1−2i−2i2i2i-2-222-11iiii−i−i−i−i1111-1-1-1-1000000002i−2i−i−iii0000000000
χ4522-2-22i−2i2i−2i00202-22i−2i02-2-22i−2i2i−2i0000002i−2i2-21+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000002−2−i2i200
χ4622-2-22i−2i2i−2i00202-22i−2i02-2-22i−2i2i−2i0000002i−2i2-21+i−1−i1−i−1+i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000−22i2−i200
χ4722-2-22i−2i2i−2i00202-22i−2i02-2-22i−2i2i−2i0000002i−2i2-2−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000−22i2−i200
χ4822-2-22i−2i2i−2i00202-22i−2i02-2-22i−2i2i−2i0000002i−2i2-2−1−i1+i−1+i1−i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000002−2−i2i200
χ4922-2-2−2i2i−2i2i00202-2−2i2i02-2-2−2i2i−2i2i000000−2i2i2-21−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000002−2i2−i200
χ5022-2-2−2i2i−2i2i00202-2−2i2i02-2-2−2i2i−2i2i000000−2i2i2-21−i−1+i1+i−1−i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000−22−i2i200
χ5122-2-2−2i2i−2i2i00202-2−2i2i02-2-2−2i2i−2i2i000000−2i2i2-2−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000−22−i2i200
χ5222-2-2−2i2i−2i2i00202-2−2i2i02-2-2−2i2i−2i2i000000−2i2i2-2−1+i1−i−1−i1+i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000002−2i2−i200
χ534444444444-24-4-4-4-44-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000220000000000000000000000000000000000000000
χ5444444444-4-4-2-44444-4-2-2-2-2-2-2-2-4-42222-2-2-2-200000000220000000000000000000000000000000000000000
χ554444-4-4-4-444-2-444-4-4-4-2-2-22222-44-2-22222-2-2000000002-20000000000000000000000000000000000000000
χ564444-4-4-4-4-4-4-24-4-4444-2-2-22222-4422-2-2-2-222000000002-20000000000000000000000000000000000000000
χ5744-4-44i−4i4i−4i0040-44−4i4i04-4-44i−4i4i−4i000000−4i4i-4400000000000000000000000000000000000000000000000000
χ5844-4-44i−4i4i−4i00-204-44i−4i0-222−2i2i−2i2i000000−2i2i-222+2i−2−2i2−2i−2+2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000000000
χ5944-4-44i−4i4i−4i00-204-44i−4i0-222−2i2i−2i2i000000−2i2i-22−2−2i2+2i−2+2i2−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000000000
χ6044-4-44i−4i4i−4i00-20-44−4i4i0-222−2i2i−2i2i0000002i−2i2-20000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000000000000000000000
χ6144-4-44i−4i4i−4i00-20-44−4i4i0-222−2i2i−2i2i0000002i−2i2-20000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000000000000000000000
χ6244-4-4−4i4i−4i4i0040-444i−4i04-4-4−4i4i−4i4i0000004i−4i-4400000000000000000000000000000000000000000000000000
χ6344-4-4−4i4i−4i4i00-204-4−4i4i0-2222i−2i2i−2i0000002i−2i-222−2i−2+2i2+2i−2−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000000000
χ6444-4-4−4i4i−4i4i00-204-4−4i4i0-2222i−2i2i−2i0000002i−2i-22−2+2i2−2i−2−2i2+2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000000000
χ6544-4-4−4i4i−4i4i00-20-444i−4i0-2222i−2i2i−2i000000−2i2i2-20000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000000000000000000000
χ6644-4-4−4i4i−4i4i00-20-444i−4i0-2222i−2i2i−2i000000−2i2i2-20000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000000000000000000000
χ674-44-44i−4i−4i4i004000000-44-44i−4i−4i4i0000000000000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000
χ684-44-44i−4i−4i4i004000000-44-44i−4i−4i4i000000000000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000
χ694-44-4−4i4i4i−4i004000000-44-4−4i4i4i−4i0000000000000000000000000000000000002+2i−2−2i002−2i−2+2i000000000000000000
χ704-44-4−4i4i4i−4i004000000-44-4−4i4i4i−4i000000000000000000000000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000
χ714-4-4444-4-44-4440000-4-4-4444-4-4004-44-4000000000000000000000000000000000000000000000000000000
χ724-4-4444-4-44-4-240000-422-2-2-22200-22-220000000000000000000000i6−i6i6−i6i6−i6i6−i6000000000000000000000000
χ734-4-4444-4-44-4-240000-422-2-2-22200-22-220000000000000000000000−i6i6−i6i6−i6i6−i6i6000000000000000000000000
χ744-4-4444-4-4-444-400004-4-4444-4-400-44-44000000000000000000000000000000000000000000000000000000
χ754-4-4444-4-4-44-2-40000422-2-2-222002-22-200000000000000000000006−6−666−6−66000000000000000000000000
χ764-4-4444-4-4-44-2-40000422-2-2-222002-22-20000000000000000000000−666−6−666−6000000000000000000000000
χ774-4-44-4-4444-44-400004-4-44-4-444004-4-44000000000000000000000000000000000000000000000000000000
χ784-4-44-4-4444-4-2-40000422-222-2-200-222-200000000000000000000006−6−66−666−6000000000000000000000000
χ794-4-44-4-4444-4-2-40000422-222-2-200-222-20000000000000000000000−666−66−6−66000000000000000000000000
χ804-4-44-4-444-44440000-4-4-44-4-44400-444-4000000000000000000000000000000000000000000000000000000
χ814-4-44-4-444-44-240000-422-222-2-2002-2-220000000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ824-4-44-4-444-44-240000-422-222-2-2002-2-220000000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ838-88-88i−8i−8i8i00-40000004-44−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ848-88-8−8i8i8i−8i00-40000004-444i−4i−4i4i000000000000000000000000000000000000000000000000000000000000

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