Finite Group Databasebeta

← Group #10693688

Character table — Group #10693688

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order122244443444444446661212121224121212121212121268888888812242424242424242424242424242424248888888888242424248888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1i−ii−i11-1-11ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−ii−iii−i−i11-1-1ii−i−i1-1
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1i−ii−i11-1-11ii−i−iii−i−i1111-1-1-1-1−i−i−i−iiiiii−iii−i−i-1-111−i−iii-11
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1i−ii−i-1-1111ii−i−iii−i−i-1-1-1-11111iiii−i−i−i−i−ii−i−iii11-1-1−i−iii-11
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1i−ii−i-1-1111ii−i−iii−i−i-1-1-1-11111−i−i−i−iiiii−ii−i−iii-1-111ii−i−i1-1
χ131111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1−ii−ii11-1-11−i−iii−i−iii1111-1-1-1-1iiii−i−i−i−i−ii−i−iii-1-111ii−i−i-11
χ141111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1−ii−ii11-1-11−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−ii−i−iii11-1-1−i−iii1-1
χ151111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1−ii−ii-1-1111−i−iii−i−iii-1-1-1-11111iiii−i−i−i−ii−iii−i−i-1-111−i−iii1-1
χ161111-1-1-1-111111-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1−ii−ii-1-1111−i−iii−i−iii-1-1-1-11111−i−i−i−iiiiii−iii−i−i11-1-1ii−i−i-11
χ1722222222222-2-222-2-22222222-2-2-2-222-2-222-222-2-20000-22222-2-2-2-200000000000000000000000000000000
χ1822222222222-2-222-2-22222222-2-2-2-222-2-222-2-2-2220000-2-2-2-2-2222200000000000000000000000000000000
χ19222222222-2-222-2-2222222222-2-222-2-222-2-2-200000000-2000000000000000022-2-222-2-20000000000000000
χ20222222222-2-222-2-2222222222-2-222-2-222-2-2-200000000-20000000000000000-2-222-2-2220000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-220000000020000000000000000000000000000002i−2i2i−2i000000
χ22222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22000000002000000000000000000000000000000−2i2i−2i2i000000
χ2322222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ2422222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ2522222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-22222-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-111111111111111110000000022-1-1-1-10000000000
χ2722222222-122-2-222-2-2-1-1-1-1-1-1-1-2-211-1-111-1-1122-2-200001-1-1-1-11111−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ2822222222-122-2-222-2-2-1-1-1-1-1-1-1-2-211-1-111-1-1122-2-200001-1-1-1-11111i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ2922222222-122-2-222-2-2-1-1-1-1-1-1-1-2-211-1-111-1-11-2-222000011111-1-1-1-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3022222222-122-2-222-2-2-1-1-1-1-1-1-1-2-211-1-111-1-11-2-222000011111-1-1-1-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-2-2-2-222222-2-2-2-22-2-2-2-2-2222222i−2i−2i2i0000-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ322222-2-2-2-2222-2-2-2-222222-2-2-2-22-2-2-2-2-222222−2i2i2i−2i0000-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ332222-2-2-2-22-2-22222-2-2222-2-2-2-22-22222-2-2-2-2200000000-200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ342222-2-2-2-22-2-22222-2-2222-2-2-2-22-22222-2-2-2-2200000000-20000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ352222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-22222-2-2-20000000020000000000000000000000000000002i−2i−2i2i000000
χ362222-2-2-2-22-2-2-2-22222222-2-2-2-2-22-2-22222-2-2-2000000002000000000000000000000000000000−2i2i2i−2i000000
χ372222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-11111-1-112i−2i2i−2i22-2-2-1−i−iii−i−iii-1-1-1-11111000000002i−2i−i−iii0000000000
χ382222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-11111-1-112i−2i2i−2i-2-222-1−i−iii−i−iii1111-1-1-1-100000000−2i2iii−i−i0000000000
χ392222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-11111-1-11−2i2i−2i2i22-2-2-1ii−i−iii−i−i-1-1-1-1111100000000−2i2iii−i−i0000000000
χ402222-2-2-2-2-12222-2-2-2-2-1-1-11111-22-1-11111-1-11−2i2i−2i2i-2-222-1ii−i−iii−i−i1111-1-1-1-1000000002i−2i−i−iii0000000000
χ412222-2-2-2-2-122-2-2-2-222-1-1-111112-21111-1-1-1-1-12i−2i−2i2i00001−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300000000003−3−330000000000
χ422222-2-2-2-2-122-2-2-2-222-1-1-111112-21111-1-1-1-1-12i−2i−2i2i00001−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000000000−333−30000000000
χ432222-2-2-2-2-122-2-2-2-222-1-1-111112-21111-1-1-1-1-1−2i2i2i−2i00001ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000000000−333−30000000000
χ442222-2-2-2-2-122-2-2-2-222-1-1-111112-21111-1-1-1-1-1−2i2i2i−2i00001ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300000000003−3−330000000000
χ4522-2-22i−2i2i−2i2002-2002i−2i2-2-22i−2i2i−2i002-2002i−2i00000002−2−i2i20000000002−22−2−i2i2−i2i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000001+i−1−i1−i−1+i00
χ4622-2-22i−2i2i−2i2002-2002i−2i2-2-22i−2i2i−2i002-2002i−2i00000002−2−i2i20000000002−22−2−i2i2−i2i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130000000000−1−i1+i−1+i1−i00
χ4722-2-22i−2i2i−2i2002-2002i−2i2-2-22i−2i2i−2i002-2002i−2i0000000−22i2−i2000000000−22−22i2−i2i2−i2002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130000000000−1−i1+i−1+i1−i00
χ4822-2-22i−2i2i−2i2002-2002i−2i2-2-22i−2i2i−2i002-2002i−2i0000000−22i2−i2000000000−22−22i2−i2i2−i200−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000001+i−1−i1−i−1+i00
χ4922-2-2−2i2i−2i2i2002-200−2i2i2-2-2−2i2i−2i2i002-200−2i2i00000002−2i2−i20000000002−22−2i2−i2i2−i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000001−i−1+i1+i−1−i00
χ5022-2-2−2i2i−2i2i2002-200−2i2i2-2-2−2i2i−2i2i002-200−2i2i00000002−2i2−i20000000002−22−2i2−i2i2−i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ230000000000−1+i1−i−1−i1+i00
χ5122-2-2−2i2i−2i2i2002-200−2i2i2-2-2−2i2i−2i2i002-200−2i2i0000000−22−i2i2000000000−22−22−i2i2−i2i200−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230000000000−1+i1−i−1−i1+i00
χ5222-2-2−2i2i−2i2i2002-200−2i2i2-2-2−2i2i−2i2i002-200−2i2i0000000−22−i2i2000000000−22−22−i2i2−i2i2002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000001−i−1+i1+i−1−i00
χ5344444444-2-4-444-4-444-2-2-2-2-2-2-2-4-4-2-222-2-22220000000020000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-24422222222-200000000-20000000000000000000000000000000000000000
χ554444-4-4-4-4-2-4-44444-4-4-2-2-222224-4-2-2-2-22222-20000000020000000000000000000000000000000000000000
χ564444-4-4-4-4-2-4-4-4-44444-2-2-22222-4422-2-2-2-222200000000-20000000000000000000000000000000000000000
χ5744-4-44i−4i4i−4i400-4400−4i4i4-4-44i−4i4i−4i00-4400−4i4i0000000000000000000000000000000000000000000000000000
χ5844-4-44i−4i4i−4i-2004-4004i−4i-222−2i2i−2i2i00-2200−2i2i000000022−22−2i22i2000000000−22−22i2−i2i2−i2000000000000000000000000
χ5944-4-44i−4i4i−4i-2004-4004i−4i-222−2i2i−2i2i00-2200−2i2i0000000−22222i2−2i20000000002−22−2−i2i2−i2i2000000000000000000000000
χ6044-4-44i−4i4i−4i-200-4400−4i4i-222−2i2i−2i2i002-2002i−2i00000000000000000000i6−i6−i6i66−6−66000000000000000000000000
χ6144-4-44i−4i4i−4i-200-4400−4i4i-222−2i2i−2i2i002-2002i−2i00000000000000000000−i6i6i6−i6−666−6000000000000000000000000
χ6244-4-4−4i4i−4i4i400-44004i−4i4-4-4−4i4i−4i4i00-44004i−4i0000000000000000000000000000000000000000000000000000
χ6344-4-4−4i4i−4i4i-2004-400−4i4i-2222i−2i2i−2i00-22002i−2i000000022−222i2−2i2000000000−22−22−i2i2−i2i2000000000000000000000000
χ6444-4-4−4i4i−4i4i-2004-400−4i4i-2222i−2i2i−2i00-22002i−2i0000000−2222−2i22i20000000002−22−2i2−i2i2−i2000000000000000000000000
χ6544-4-4−4i4i−4i4i-200-44004i−4i-2222i−2i2i−2i002-200−2i2i00000000000000000000i6−i6−i6i6−666−6000000000000000000000000
χ6644-4-4−4i4i−4i4i-200-44004i−4i-2222i−2i2i−2i002-200−2i2i00000000000000000000−i6i6i6−i66−6−66000000000000000000000000
χ674-44-44i−4i−4i4i44-4004i−4i00-44-44i−4i−4i4i00004i−4i004-400000000000000000000000000000000000000000000000000
χ684-44-44i−4i−4i4i4-4400−4i4i00-44-44i−4i−4i4i0000−4i4i00-4400000000000000000000000000000000000000000000000000
χ694-44-44i−4i−4i4i-24-4004i−4i002-22−2i2i2i−2i0000−2i2i00-22000000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000000000
χ704-44-44i−4i−4i4i-24-4004i−4i002-22−2i2i2i−2i0000−2i2i00-2200000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000000000
χ714-44-44i−4i−4i4i-2-4400−4i4i002-22−2i2i2i−2i00002i−2i002-20000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000000000
χ724-44-44i−4i−4i4i-2-4400−4i4i002-22−2i2i2i−2i00002i−2i002-200000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000
χ734-44-4−4i4i4i−4i44-400−4i4i00-44-4−4i4i4i−4i0000−4i4i004-400000000000000000000000000000000000000000000000000
χ744-44-4−4i4i4i−4i4-44004i−4i00-44-4−4i4i4i−4i00004i−4i00-4400000000000000000000000000000000000000000000000000
χ754-44-4−4i4i4i−4i-24-400−4i4i002-222i−2i−2i2i00002i−2i00-2200000000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000000000
χ764-44-4−4i4i4i−4i-24-400−4i4i002-222i−2i−2i2i00002i−2i00-22000000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000000000
χ774-44-4−4i4i4i−4i-2-44004i−4i002-222i−2i−2i2i0000−2i2i002-200000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000000000
χ784-44-4−4i4i4i−4i-2-44004i−4i002-222i−2i−2i2i0000−2i2i002-20000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000000000
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.