Finite Group Databasebeta

← Group #10694554

Character table — Group #10694554

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122244442234444446661212121244661212121212128888888812122424242424242424242424242424242488888888246612124444888844
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
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
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
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-111-1-1ii−i−iii−i−i1-1
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1ii−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111111-111-1-1−i−iii−i−iii-11
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1ii−i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-11-1-111ii−i−i−i−iii-11
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1ii−i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11-1-111−i−iiiii−i−i1-1
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1−i−iiiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-11-1-111−i−iiiii−i−i-11
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1−i−iiiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11-1-111ii−i−i−i−iii1-1
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-111-1-1−i−iii−i−iii1-1
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-11-1-1-11111-1-1−i−iii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111111-111-1-1ii−i−iii−i−i-11
χ1722222222222-2-222-2-22222222-2-222-2-222-2-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ1822222222222-2-222-2-22222222-2-222-2-222-2-200000000-2-20000000000000000-2-222-2-2220000000000000000
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
χ2322222222-2-2222-2-2222222222-2-2-2-222-2-2222-22-20000-2-222-2-222-2-200000000000000000000000000000000
χ2422222222-2-2222-2-2222222222-2-2-2-222-2-222-22-220000-2-2-2-222-2-22200000000000000000000000000000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000000000000000002i−2i2i−2i000000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-20000000022000000000000000000000000000000−2i2i−2i2i000000
χ2722222222-2-2-122-2-222-1-1-1-1-1-1-1-2-211-1-111-1-12-22-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ2822222222-2-2-122-2-222-1-1-1-1-1-1-1-2-211-1-111-1-12-22-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ2922222222-2-2-122-2-222-1-1-1-1-1-1-1-2-211-1-111-1-1-22-2200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3022222222-2-2-122-2-222-1-1-1-1-1-1-1-2-211-1-111-1-1-22-2200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ312222-2-2-2-222222-2-2-2-2222-2-2-2-2-222222-2-2-2-22i−2i−2i2i0000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ322222-2-2-2-222222-2-2-2-2222-2-2-2-2-222222-2-2-2-2−2i2i2i−2i0000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-2-2-222000000002-20000000000000000000000000000002-2-22000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-22-222-2-2-2-222000000002-2000000000000000000000000000000-222-2000000
χ352222-2-2-2-222-122-2-2-2-2-1-1-11111-22-1-1-1-111112i−2i−2i2i00001-1−i−iiiii−i−i33−3−3−3−3330000000000−i3i3i3−i30000000000
χ362222-2-2-2-222-122-2-2-2-2-1-1-11111-22-1-1-1-111112i−2i−2i2i00001-1−i−iiiii−i−i−3−33333−3−30000000000i3−i3−i3i30000000000
χ372222-2-2-2-222-122-2-2-2-2-1-1-11111-22-1-1-1-11111−2i2i2i−2i00001-1ii−i−i−i−iii33−3−3−3−3330000000000i3−i3−i3i30000000000
χ382222-2-2-2-222-122-2-2-2-2-1-1-11111-22-1-1-1-11111−2i2i2i−2i00001-1ii−i−i−i−iii−3−33333−3−30000000000−i3i3i3−i30000000000
χ392222-2-2-2-2-2-22-2-22222222-2-2-2-2-22-2-2-2-2222200000000-22000000000000000022-2-2-2-2220000000000000000
χ402222-2-2-2-2-2-22-2-22222222-2-2-2-2-22-2-2-2-2222200000000-220000000000000000-2-22222-2-20000000000000000
χ412222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-1-1112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii000000002-2-1-1110000000000
χ422222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-1-1112i2i−2i−2i−2i−2i2i2i-11−i−i−i−iiiiiiiii−i−i−i−i00000000-2211-1-10000000000
χ432222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-1-111−2i−2i2i2i2i2i−2i−2i-11iiii−i−i−i−i−i−i−i−iiiii00000000-2211-1-10000000000
χ442222-2-2-2-2-2-2-12222-2-2-1-1-111112-211-1-1-1-111−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i000000002-2-1-1110000000000
χ4522-2-222-2-2-222002-200-2-2222-2-2002-2002-2000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i00000000002−22−200
χ4622-2-222-2-2-222002-200-2-2222-2-2002-2002-2000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i0000000000−22−2200
χ4722-2-222-2-2-222002-200-2-2222-2-2002-2002-2000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i0000000000−22−2200
χ4822-2-222-2-2-222002-200-2-2222-2-2002-2002-2000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i00000000002−22−200
χ4922-2-2-2-2222-22002-200-2-22-2-22200-22002-20000002−2−2200000000002−22−2−22−22002i−2i00−2i2i0000000000i2−i2−i2i200
χ5022-2-2-2-2222-22002-200-2-22-2-22200-22002-20000002−2−2200000000002−22−2−22−2200−2i2i002i−2i0000000000−i2i2i2−i200
χ5122-2-2-2-2222-22002-200-2-22-2-22200-22002-2000000−222−20000000000−22−222−22−2002i−2i00−2i2i0000000000−i2i2i2−i200
χ5222-2-2-2-2222-22002-200-2-22-2-22200-22002-2000000−222−20000000000−22−222−22−200−2i2i002i−2i0000000000i2−i2−i2i200
χ534444444444-2-4-444-4-4-2-2-2-2-2-2-2-4-4-2-222-2-22200000000220000000000000000000000000000000000000000
χ5444444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000
χ554444-4-4-4-444-2-4-4-4-444-2-2-222224-4-2-22222-2-200000000-220000000000000000000000000000000000000000
χ564444-4-4-4-4-4-4-2-4-44444-2-2-22222-442222-2-2-2-2000000002-20000000000000000000000000000000000000000
χ5744-4-444-4-44-4400-4400-4-4444-4-400-4400-440000000000000000000000000000000000000000000000000000
χ5844-4-444-4-44-4-200-440022-2-2-222002-2002-2000000000000000000006−6−666−6−66000000000000000000000000
χ5944-4-444-4-44-4-200-440022-2-2-222002-2002-200000000000000000000−666−6−666−6000000000000000000000000
χ6044-4-444-4-4-44-2004-40022-2-2-22200-2200-22000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ6144-4-444-4-4-44-2004-40022-2-2-22200-2200-220000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ6244-4-4-4-4444-4-2004-40022-222-2-2002-200-2200000022−22−22220000000000−22−222−22−2000000000000000000000000
χ6344-4-4-4-4444-4-2004-40022-222-2-2002-200-22000000−222222−2200000000002−22−2−22−22000000000000000000000000
χ6444-4-4-4-444-44400-4400-4-44-4-444004-400-440000000000000000000000000000000000000000000000000000
χ6544-4-4-4-444-44-200-440022-222-2-200-22002-200000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ6644-4-4-4-444-44-200-440022-222-2-200-22002-200000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ674-44-44i−4i4i−4i0040000004-4-44i−4i4i−4i00000000000000000000000000000000000022−2200−2i22i2000000000000000000
χ684-44-44i−4i4i−4i0040000004-4-44i−4i4i−4i000000000000000000000000000000000000−2222002i2−2i2000000000000000000
χ694-44-4−4i4i−4i4i0040000004-4-4−4i4i−4i4i00000000000000000000000000000000000022−22002i2−2i2000000000000000000
χ704-44-4−4i4i−4i4i0040000004-4-4−4i4i−4i4i000000000000000000000000000000000000−222200−2i22i2000000000000000000
χ714-4-444i−4i−4i4i0044-4004i−4i-44-44i−4i−4i4i00004-4004i−4i00000000000000000000000000000000000000000000000000
χ724-4-444i−4i−4i4i004-4400−4i4i-44-44i−4i−4i4i0000-4400−4i4i00000000000000000000000000000000000000000000000000
χ734-4-444i−4i−4i4i00-24-4004i−4i2-22−2i2i2i−2i0000-2200−2i2i000000000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000000000
χ744-4-444i−4i−4i4i00-24-4004i−4i2-22−2i2i2i−2i0000-2200−2i2i0000000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000000000
χ754-4-444i−4i−4i4i00-2-4400−4i4i2-22−2i2i2i−2i00002-2002i−2i00000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000000000
χ764-4-444i−4i−4i4i00-2-4400−4i4i2-22−2i2i2i−2i00002-2002i−2i0000000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000000000
χ774-4-44−4i4i4i−4i0044-400−4i4i-44-4−4i4i4i−4i00004-400−4i4i00000000000000000000000000000000000000000000000000
χ784-4-44−4i4i4i−4i004-44004i−4i-44-4−4i4i4i−4i0000-44004i−4i00000000000000000000000000000000000000000000000000
χ794-4-44−4i4i4i−4i00-24-400−4i4i2-222i−2i−2i2i0000-22002i−2i0000000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000000000
χ804-4-44−4i4i4i−4i00-24-400−4i4i2-222i−2i−2i2i0000-22002i−2i000000000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000000000
χ814-4-44−4i4i4i−4i00-2-44004i−4i2-222i−2i−2i2i00002-200−2i2i0000000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000000000
χ824-4-44−4i4i4i−4i00-2-44004i−4i2-222i−2i−2i2i00002-200−2i2i00000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000000000
χ838-88-88i−8i8i−8i00-4000000-444−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ848-88-8−8i8i−8i8i00-4000000-4444i−4i4i−4i000000000000000000000000000000000000000000000000000000000000

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