Finite Group Databasebeta

← Group #10691285

Character table — Group #10691285

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12224444223444444666121212124466121212121212888888881212242424242424242424242424242424248888888888242424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-1111-1-1ii−i−i1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−ii−iii−i−i1-11-1ii−i−i1-1
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-1111-1-1ii−i−i1-1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiii−iii−i−i-11-11−i−iii-11
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-1111-1-1−i−iii1-1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−ii−i−iii-11-11ii−i−i-11
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-1111-1-1−i−iii1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−ii−i−iii1-11-1−i−iii1-1
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11-1-111ii−i−i1-1iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i−ii−i−iii1-11-1−i−iii-11
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11-1-111ii−i−i1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−ii−i−iii-11-11ii−i−i1-1
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11-1-111−i−iii1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−ii−iii−i−i-11-11−i−iii1-1
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11-1-111−i−iii1-1−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiiii−iii−i−i1-11-1ii−i−i-11
χ17222222222222-2-22-2-22222222-2-2222-2-2-2-2200000000-2-200000000000000000000000000000022-2-2000000
χ18222222222222-2-22-2-22222222-2-2222-2-2-2-2200000000-2-2000000000000000000000000000000-2-222000000
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
χ202222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
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
χ2322222222-2-22-222-2222222222-2-2-2-2-22222-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ2422222222-2-22-222-2222222222-2-2-2-2-22222-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200002i−2i2i−2i222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000−2i2i−2i2i22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ2722222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100002i−2i2i−2i-1-1−i−iii−i−iii33−3−333−3−30000000000−i3i3−i3i30000000000
χ2822222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-1221111111100002i−2i2i−2i-1-1−i−iii−i−iii−3−333−3−3330000000000i3−i3i3−i30000000000
χ2922222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122111111110000−2i2i−2i2i-1-1ii−i−iii−i−i33−3−333−3−30000000000i3−i3i3−i30000000000
χ3022222222-2-2-1-2-2-2-2-2-2-1-1-1-1-1-1-122111111110000−2i2i−2i2i-1-1ii−i−iii−i−i−3−333−3−3330000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-222-2-2-2222-2-2-2-2-2222-222-2-2-200000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2222-222-2-2-2222-2-2-2-2-2222-222-2-2-200000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-2-222-200002-2-222-222-2-2-2-22200000000000000000000000000000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-2-222-20000-222-22-2-2-22222-2-200000000000000000000000000000000
χ352222-2-2-2-222-1-2-2-2-222-1-1-111112-2-1-1111-1-1100002-2-22-11-1-11111-1-133−3−3−3−3330000000000−333−30000000000
χ362222-2-2-2-222-1-2-2-2-222-1-1-111112-2-1-1111-1-1100002-2-22-11-1-11111-1-1−3−33333−3−300000000003−3−330000000000
χ372222-2-2-2-222-1-2-2-2-222-1-1-111112-2-1-1111-1-110000-222-2-1111-1-1-1-11133−3−3−3−33300000000003−3−330000000000
χ382222-2-2-2-222-1-2-2-2-222-1-1-111112-2-1-1111-1-110000-222-2-1111-1-1-1-111−3−33333−3−30000000000−333−30000000000
χ392222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-22-2-222200000000-220000000000000000000000000000002-2-22000000
χ402222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-22-2-222200000000-22000000000000000000000000000000-222-2000000
χ412222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-111-122-2-22i2i−2i−2i-11−i−i−i−iiiii-1-1-1-11111000000002i−2i−i−iii0000000000
χ422222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-111-122-2-2−2i−2i2i2i-11iiii−i−i−i−i-1-1-1-1111100000000−2i2iii−i−i0000000000
χ432222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-111-1-2-2222i2i−2i−2i-11−i−i−i−iiiii1111-1-1-1-100000000−2i2iii−i−i0000000000
χ442222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-111-1-2-222−2i−2i2i2i-11iiii−i−i−i−i1111-1-1-1-1000000002i−2i−i−iii0000000000
χ452-22-22i−2i2i−2i00202-202i−2i2-2-22i−2i2i−2i000002-22i−2i02−2−i2i2000000000000002−22−2−i2i2−i2i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000001+i−1−i1−i−1+i00
χ462-22-22i−2i2i−2i00202-202i−2i2-2-22i−2i2i−2i000002-22i−2i02−2−i2i2000000000000002−22−2−i2i2−i2i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000−1−i1+i−1+i1−i00
χ472-22-22i−2i2i−2i00202-202i−2i2-2-22i−2i2i−2i000002-22i−2i0−22i2−i200000000000000−22−22i2−i2i2−i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000−1−i1+i−1+i1−i00
χ482-22-22i−2i2i−2i00202-202i−2i2-2-22i−2i2i−2i000002-22i−2i0−22i2−i200000000000000−22−22i2−i2i2−i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000001+i−1−i1−i−1+i00
χ492-22-2−2i2i−2i2i00202-20−2i2i2-2-2−2i2i−2i2i000002-2−2i2i02−2i2−i2000000000000002−22−2i2−i2i2−i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000001−i−1+i1+i−1−i00
χ502-22-2−2i2i−2i2i00202-20−2i2i2-2-2−2i2i−2i2i000002-2−2i2i02−2i2−i2000000000000002−22−2i2−i2i2−i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000−1+i1−i−1−i1+i00
χ512-22-2−2i2i−2i2i00202-20−2i2i2-2-2−2i2i−2i2i000002-2−2i2i0−22−i2i200000000000000−22−22−i2i2−i2i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000−1+i1−i−1−i1+i00
χ522-22-2−2i2i−2i2i00202-20−2i2i2-2-2−2i2i−2i2i000002-2−2i2i0−22−i2i200000000000000−22−22−i2i2−i2i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000001−i−1+i1+i−1−i00
χ534444444444-24-4-44-4-4-2-2-2-2-2-2-2-4-4-2-2-22222-200000000220000000000000000000000000000000000000000
χ5444444444-4-4-2-444-444-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000220000000000000000000000000000000000000000
χ554444-4-4-4-444-2-444-4-4-4-2-2-22222-44-2-22-2-2222000000002-20000000000000000000000000000000000000000
χ564444-4-4-4-4-4-4-24-4-4444-2-2-22222-4422-222-2-2-2000000002-20000000000000000000000000000000000000000
χ5744-4-444-4-44-44-400400-44-444-4-4004-4-40000400000000000000000000000000000000000000000000000000
χ5844-4-444-4-44-4-2-4004002-22-2-22200-2220000-200000000006−66−66−66−600000000000000000000000000000000
χ5944-4-444-4-44-4-2-4004002-22-2-22200-2220000-20000000000−66−66−66−6600000000000000000000000000000000
χ6044-4-444-4-4-444400-400-44-444-4-400-4440000-400000000000000000000000000000000000000000000000000
χ6144-4-444-4-4-44-2400-4002-22-2-222002-2-2000020000000000i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ6244-4-444-4-4-44-2400-4002-22-2-222002-2-2000020000000000−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ6344-4-4-4-4444-44400-400-44-4-4-444004-440000-400000000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4-2400-4002-2222-2-200-22-20000200000000006−6−66−666−600000000000000000000000000000000
χ6544-4-4-4-4444-4-2400-4002-2222-2-200-22-2000020000000000−666−66−6−6600000000000000000000000000000000
χ6644-4-4-4-444-444-400400-44-4-4-44400-44-40000400000000000000000000000000000000000000000000000000
χ6744-4-4-4-444-44-2-4004002-2222-2-2002-220000-20000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ6844-4-4-4-444-44-2-4004002-2222-2-2002-220000-20000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ694-44-44i−4i4i−4i0040-440−4i4i4-4-44i−4i4i−4i00000-44−4i4i000000000000000000000000000000000000000000000000000
χ704-44-44i−4i4i−4i00-204-404i−4i-222−2i2i−2i2i00000-22−2i2i022−22−2i22i200000000000000−22−22i2−i2i2−i2000000000000000000000000
χ714-44-44i−4i4i−4i00-204-404i−4i-222−2i2i−2i2i00000-22−2i2i0−22222i2−2i2000000000000002−22−2−i2i2−i2i2000000000000000000000000
χ724-44-44i−4i4i−4i00-20-440−4i4i-222−2i2i−2i2i000002-22i−2i00000000000000000006−6−66−i6i6i6−i6000000000000000000000000
χ734-44-44i−4i4i−4i00-20-440−4i4i-222−2i2i−2i2i000002-22i−2i0000000000000000000−666−6i6−i6−i6i6000000000000000000000000
χ744-44-4−4i4i−4i4i0040-4404i−4i4-4-4−4i4i−4i4i00000-444i−4i000000000000000000000000000000000000000000000000000
χ754-44-4−4i4i−4i4i00-204-40−4i4i-2222i−2i2i−2i00000-222i−2i022−222i2−2i200000000000000−22−22−i2i2−i2i2000000000000000000000000
χ764-44-4−4i4i−4i4i00-204-40−4i4i-2222i−2i2i−2i00000-222i−2i0−2222−2i22i2000000000000002−22−2i2−i2i2−i2000000000000000000000000
χ774-44-4−4i4i−4i4i00-20-4404i−4i-2222i−2i2i−2i000002-2−2i2i00000000000000000006−6−66i6−i6−i6i6000000000000000000000000
χ784-44-4−4i4i−4i4i00-20-4404i−4i-2222i−2i2i−2i000002-2−2i2i0000000000000000000−666−6−i6i6i6−i6000000000000000000000000
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.