Finite Group Databasebeta

← Group #10693709

Character table — Group #10693709

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12224444223444444666121212124466121212121212888888881212242424242424242424242424242424248888888888242424244444888844
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
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11i−ii−i11-1-11-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−ii−iii−i−iii−i−i11-1-11-1
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11i−ii−i11-1-11-1ii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiiii−iii−i−i−i−iii-1-111-11
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11i−ii−i-1-1111-1ii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i−ii−i−iii−i−iii11-1-1-11
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11i−ii−i-1-1111-1ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−ii−i−iiiii−i−i-1-1111-1
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11−ii−ii11-1-11-1−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−i−ii−i−iiiii−i−i-1-111-11
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11−ii−ii11-1-11-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−ii−i−iii−i−iii11-1-11-1
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11−ii−ii-1-1111-1−i−iii−i−iii-1-1-1-11111iiii−i−i−i−ii−iii−i−i−i−iii-1-1111-1
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-1111-1-11−ii−ii-1-1111-1−i−iii−i−iii-1-1-1-11111−i−i−i−iiiiii−iii−i−iii−i−i11-1-1-11
χ172222222222222-2-2-2-22222222-2-2222-2-2-2-2222-2-20000-2-22222-2-2-2-200000000000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2222-2-2-2-22-2-2220000-2-2-2-2-2-2222200000000000000000000000000000000
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
χ232222222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2000011-1-1-1-11111−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ242222222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-11111-122-2-2000011-1-1-1-11111i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ252222222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2220000111111-1-1-1-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ262222222222-122-2-2-2-2-1-1-1-1-1-1-1-2-2-1-1-11111-1-2-2220000111111-1-1-1-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ2722222222-2-22-2-222222222222-2-2-2-2-22222-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ2822222222-2-22-2-222222222222-2-2-2-2-22222-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ2922222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000002200000000000000000000000000000000002i−2i2i−2i00
χ3022222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000000000000000000000−2i2i−2i2i00
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-2-2222-222-2-2-200000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-2-2222-222-2-2-200000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-2-222-2000000002-200000000000000000000000000000000002i−2i−2i2i00
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-2-222-2000000002-20000000000000000000000000000000000−2i2i2i−2i00
χ352222-2-2-2-2-2-2222-2-222222-2-2-2-2-22-2-22-2-22222i−2i−2i2i0000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ362222-2-2-2-2-2-2222-2-222222-2-2-2-2-22-2-22-2-2222−2i2i2i−2i0000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ372222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-111-12i−2i2i−2i22-2-2-11−i−iii−i−iii-1-1-1-11111000000002i−2i−i−iii0000000000
χ382222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-111-12i−2i2i−2i-2-222-11−i−iii−i−iii1111-1-1-1-100000000−2i2iii−i−i0000000000
χ392222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-111-1−2i2i−2i2i22-2-2-11ii−i−iii−i−i-1-1-1-1111100000000−2i2iii−i−i0000000000
χ402222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-111-1−2i2i−2i2i-2-222-11ii−i−iii−i−i1111-1-1-1-1000000002i−2i−i−iii0000000000
χ412222-2-2-2-2-2-2-122-2-222-1-1-11111-2211-111-1-1-12i−2i−2i2i00001-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300000000003−3−330000000000
χ422222-2-2-2-2-2-2-122-2-222-1-1-11111-2211-111-1-1-12i−2i−2i2i00001-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000000000−333−30000000000
χ432222-2-2-2-2-2-2-122-2-222-1-1-11111-2211-111-1-1-1−2i2i2i−2i00001-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000000000−333−30000000000
χ442222-2-2-2-2-2-2-122-2-222-1-1-11111-2211-111-1-1-1−2i2i2i−2i00001-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300000000003−3−330000000000
χ452-22-22i−2i2i−2i002002-22i−2i2-2-22i−2i2i−2i000002-22i−2i000002−2−i2i200000000002−22−2−i2i2−i2i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000001−i−1+i1+i−1−i000000
χ462-22-22i−2i2i−2i002002-22i−2i2-2-22i−2i2i−2i000002-22i−2i000002−2−i2i200000000002−22−2−i2i2−i2i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000−1+i1−i−1−i1+i000000
χ472-22-22i−2i2i−2i002002-22i−2i2-2-22i−2i2i−2i000002-22i−2i00000−22i2−i20000000000−22−22i2−i2i2−i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000−1+i1−i−1−i1+i000000
χ482-22-22i−2i2i−2i002002-22i−2i2-2-22i−2i2i−2i000002-22i−2i00000−22i2−i20000000000−22−22i2−i2i2−i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000001−i−1+i1+i−1−i000000
χ492-22-2−2i2i−2i2i002002-2−2i2i2-2-2−2i2i−2i2i000002-2−2i2i000002−2i2−i200000000002−22−2i2−i2i2−i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000001+i−1−i1−i−1+i000000
χ502-22-2−2i2i−2i2i002002-2−2i2i2-2-2−2i2i−2i2i000002-2−2i2i000002−2i2−i200000000002−22−2i2−i2i2−i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000−1−i1+i−1+i1−i000000
χ512-22-2−2i2i−2i2i002002-2−2i2i2-2-2−2i2i−2i2i000002-2−2i2i00000−22−i2i20000000000−22−22−i2i2−i2i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000−1−i1+i−1+i1−i000000
χ522-22-2−2i2i−2i2i002002-2−2i2i2-2-2−2i2i−2i2i000002-2−2i2i00000−22−i2i20000000000−22−22−i2i2−i2i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000001+i−1−i1−i−1+i000000
χ5344444444-4-4-2-4-44444-2-2-2-2-2-2-2-4-4222-2-2-2-2200000000220000000000000000000000000000000000000000
χ5444444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000
χ554444-4-4-4-444-2-4-444-4-4-2-2-22222-44-2-22-2-2222000000002-20000000000000000000000000000000000000000
χ564444-4-4-4-444-2-4-4-4-444-2-2-222224-4-2-2222-2-2200000000-220000000000000000000000000000000000000000
χ5744-4-444-4-44-44-440000-44-444-4-4004-4-40000400000000000000000000000000000000000000000000000000
χ5844-4-444-4-44-4-2-4400002-22-2-22200-2220000-20000000000000023−2323−2300000000000000000000000000000000
χ5944-4-444-4-44-4-2-4400002-22-2-22200-2220000-200000000000000−2323−232300000000000000000000000000000000
χ6044-4-444-4-4-4444-40000-44-444-4-400-4440000-400000000000000000000000000000000000000000000000000
χ6144-4-444-4-4-44-24-400002-22-2-222002-2-2000020000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ6244-4-444-4-4-44-24-400002-22-2-222002-2-20000200000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ6344-4-4-4-4444-444-40000-44-4-4-444004-440000-400000000000000000000000000000000000000000000000000
χ6444-4-4-4-4444-4-24-400002-2222-2-200-22-200002000000000023−23−2323000000000000000000000000000000000000
χ6544-4-4-4-4444-4-24-400002-2222-2-200-22-2000020000000000−232323−23000000000000000000000000000000000000
χ6644-4-4-4-444-444-440000-44-4-4-44400-44-40000400000000000000000000000000000000000000000000000000
χ6744-4-4-4-444-44-2-4400002-2222-2-2002-220000-200000000000000−2i32i32i3−2i300000000000000000000000000000000
χ6844-4-4-4-444-44-2-4400002-2222-2-2002-220000-2000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ694-44-44i−4i4i−4i00400-44−4i4i4-4-44i−4i4i−4i00000-44−4i4i000000000000000000000000000000000000000000000000000
χ704-44-44i−4i4i−4i00-2004-44i−4i-222−2i2i−2i2i00000-22−2i2i0000022−22−2i22i20000000000−22−22i2−i2i2−i2000000000000000000000000
χ714-44-44i−4i4i−4i00-2004-44i−4i-222−2i2i−2i2i00000-22−2i2i00000−22222i2−2i200000000002−22−2−i2i2−i2i2000000000000000000000000
χ724-44-44i−4i4i−4i00-200-44−4i4i-222−2i2i−2i2i000002-22i−2i0000000000000000000i6−i6−i6i66−6−66000000000000000000000000
χ734-44-44i−4i4i−4i00-200-44−4i4i-222−2i2i−2i2i000002-22i−2i0000000000000000000−i6i6i6−i6−666−6000000000000000000000000
χ744-44-4−4i4i−4i4i00400-444i−4i4-4-4−4i4i−4i4i00000-444i−4i000000000000000000000000000000000000000000000000000
χ754-44-4−4i4i−4i4i00-2004-4−4i4i-2222i−2i2i−2i00000-222i−2i0000022−222i2−2i20000000000−22−22−i2i2−i2i2000000000000000000000000
χ764-44-4−4i4i−4i4i00-2004-4−4i4i-2222i−2i2i−2i00000-222i−2i00000−2222−2i22i200000000002−22−2i2−i2i2−i2000000000000000000000000
χ774-44-4−4i4i−4i4i00-200-444i−4i-2222i−2i2i−2i000002-2−2i2i0000000000000000000i6−i6−i6i6−666−6000000000000000000000000
χ784-44-4−4i4i−4i4i00-200-444i−4i-2222i−2i2i−2i000002-2−2i2i0000000000000000000−i6i6i6−i66−6−66000000000000000000000000
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.