Finite Group Databasebeta

← Group #11790601

Character table — Group #11790601

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111114444444444444444448888888899999999121212121212121212121212121212122424242424242424242424242424242436363636363636363636
order1222444433446666661212121212121212121212121212121222224444222244448888888866661212121224242424242424244488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ51111111111-1-111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ61111111111-1-111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ81111111111-1-111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1−i−iii−i−iii
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−iii−i−i-1-1-1-11111ii−i−iii−i−i1-1−i−iii−i−iii
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iii−i−iii-1-1-1-11111−i−iii−i−iii1-1ii−i−iii−i−i
χ131111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111ii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii-11ii−i−i−i−iii
χ141111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i-11−i−iiiii−i−i
χ151111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1ii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii-11−i−iiiii−i−i
χ161111-1-1-1-111-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i-11ii−i−i−i−iii
χ172222222222222222222222222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000-2-200000000
χ182222222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002200000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2200000000
χ202222-2-2-2-222-22222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000002-200000000
χ2122-2-22i2i−2i−2i22002-2-22-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-22i−2i2i−2i002-2002i−2i00000000002-2002i−2i000000000000000000
χ2222-2-22i2i−2i−2i22002-2-22-2-22i2i−2i−2i2i2i−2i−2i0000000022-2-22i−2i2i−2i00-2200−2i2i0000000000-2200−2i2i000000000000000000
χ2322-2-22i2i−2i−2i22002-2-22-2-22i2i−2i−2i2i2i−2i−2i00000000-2-222−2i2i−2i2i2-2002i−2i00000000002-2002i−2i00000000000000000000
χ2422-2-22i2i−2i−2i22002-2-22-2-22i2i−2i−2i2i2i−2i−2i00000000-2-222−2i2i−2i2i-2200−2i2i0000000000-2200−2i2i00000000000000000000
χ2522-2-2−2i−2i2i2i22002-2-22-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-2−2i2i−2i2i002-200−2i2i00000000002-200−2i2i000000000000000000
χ2622-2-2−2i−2i2i2i22002-2-22-2-2−2i−2i2i2i−2i−2i2i2i0000000022-2-2−2i2i−2i2i00-22002i−2i0000000000-22002i−2i000000000000000000
χ2722-2-2−2i−2i2i2i22002-2-22-2-2−2i−2i2i2i−2i−2i2i2i00000000-2-2222i−2i2i−2i2-200−2i2i00000000002-200−2i2i00000000000000000000
χ2822-2-2−2i−2i2i2i22002-2-22-2-2−2i−2i2i2i−2i−2i2i2i00000000-2-2222i−2i2i−2i-22002i−2i0000000000-22002i−2i00000000000000000000
χ292-22-22i−2i2i−2i2200-22-2-22-22i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i−2i2i00000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ302-22-22i−2i2i−2i2200-22-2-22-22i−2i2i−2i2i−2i2i−2i000000002-22-22i−2i−2i2i0000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ312-22-22i−2i2i−2i2200-22-2-22-22i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i2i−2i000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ322-22-22i−2i2i−2i2200-22-2-22-22i−2i2i−2i2i−2i2i−2i00000000-22-22−2i2i2i−2i00000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ332-22-2−2i2i−2i2i2200-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i2i−2i00000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ342-22-2−2i2i−2i2i2200-22-2-22-2−2i2i−2i2i−2i2i−2i2i000000002-22-2−2i2i2i−2i0000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ352-22-2−2i2i−2i2i2200-22-2-22-2−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i−2i2i000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ362-22-2−2i2i−2i2i2200-22-2-22-2−2i2i−2i2i−2i2i−2i2i00000000-22-222i−2i−2i2i00000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ372-2-222-2-222200-2-22-2-222-2-222-2-22000000002-2-2222-2-20000000000002i−2i2i−2i0000000000002i−2i2i−2i0000000000
χ382-2-222-2-222200-2-22-2-222-2-222-2-22000000002-2-2222-2-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i0000000000
χ392-2-222-2-222200-2-22-2-222-2-222-2-2200000000-222-2-2-222000000002-22-20000000000002-22-200000000000000
χ402-2-222-2-222200-2-22-2-222-2-222-2-2200000000-222-2-2-22200000000-22-22000000000000-22-2200000000000000
χ412-2-22-222-22200-2-22-2-22-222-2-222-2000000002-2-22-2-2220000000000002-2-220000000000002-2-220000000000
χ422-2-22-222-22200-2-22-2-22-222-2-222-2000000002-2-22-2-222000000000000-222-2000000000000-222-20000000000
χ432-2-22-222-22200-2-22-2-22-222-2-222-200000000-222-222-2-2000000002i−2i−2i2i0000000000002i−2i−2i2i00000000000000
χ442-2-22-222-22200-2-22-2-22-222-2-222-200000000-222-222-2-200000000−2i2i2i−2i000000000000−2i2i2i−2i00000000000000
χ45444444441-244111-2-2-2-2-2-2-2111111-2-211-2-200000000000000002222222200000000-1-1-1-1-1-1-1-10000000000
χ46444444441-244111-2-2-2-2-2-2-2111111-2-211-2-20000000000000000-2-2-2-2-2-2-2-200000000111111110000000000
χ47444444441-2-4-4111-2-2-2-2-2-2-21111-1-122-1-12200000000000000002222-2-2-2-200000000-1-1-1-111110000000000
χ48444444441-2-4-4111-2-2-2-2-2-2-21111-1-122-1-1220000000000000000-2-2-2-22222000000001111-1-1-1-10000000000
χ4944444444-2144-2-2-21111111-2-2-2-2-2-211-2-211000000002222222200000000-1-1-1-1-1-1-1-1000000000000000000
χ5044444444-2144-2-2-21111111-2-2-2-2-2-211-2-21100000000-2-2-2-2-2-2-2-20000000011111111000000000000000000
χ5144444444-21-4-4-2-2-21111111-2-2-2-222-1-122-1-10000000022-2-222-2-200000000-1-111-1-111000000000000000000
χ5244444444-21-4-4-2-2-21111111-2-2-2-222-1-122-1-100000000-2-222-2-2220000000011-1-111-1-1000000000000000000
χ534444-4-4-4-41-24-4111-2-2-22222-1-1-1-111-2-2-1-12200000000000000002i2i−2i−2i2i2i−2i−2i00000000−i−iii−i−iii0000000000
χ544444-4-4-4-41-24-4111-2-2-22222-1-1-1-111-2-2-1-1220000000000000000−2i−2i2i2i−2i−2i2i2i00000000ii−i−iii−i−i0000000000
χ554444-4-4-4-41-2-44111-2-2-22222-1-1-1-1-1-12211-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000−i−iiiii−i−i0000000000
χ564444-4-4-4-41-2-44111-2-2-22222-1-1-1-1-1-12211-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000ii−i−i−i−iii0000000000
χ574444-4-4-4-4-214-4-2-2-2111-1-1-1-12222-2-21122-1-1000000002222-2-2-2-200000000-1-1-1-11111000000000000000000
χ584444-4-4-4-4-214-4-2-2-2111-1-1-1-12222-2-21122-1-100000000-2-2-2-22222000000001111-1-1-1-1000000000000000000
χ594444-4-4-4-4-21-44-2-2-2111-1-1-1-1222222-1-1-2-2110000000022-2-2-2-22200000000-1-11111-1-1000000000000000000
χ604444-4-4-4-4-21-44-2-2-2111-1-1-1-1222222-1-1-2-21100000000-2-22222-2-20000000011-1-1-1-111000000000000000000
χ6144-4-44i4i−4i−4i-2100-2221-1-1ii−i−i−2i−2i2i2i003-3003i−3i000000002-22-22i−2i2i−2i00000000-11-11−ii−ii000000000000000000
χ6244-4-44i4i−4i−4i-2100-2221-1-1ii−i−i−2i−2i2i2i003-3003i−3i00000000-22-22−2i2i−2i2i000000001-11-1i−ii−i000000000000000000
χ6344-4-44i4i−4i−4i-2100-2221-1-1ii−i−i−2i−2i2i2i00-3300−3i3i000000002-2-222i−2i−2i2i00000000-111-1−iii−i000000000000000000
χ6444-4-44i4i−4i−4i-2100-2221-1-1ii−i−i−2i−2i2i2i00-3300−3i3i00000000-222-2−2i2i2i−2i000000001-1-11i−i−ii000000000000000000
χ6544-4-4−4i−4i4i4i-2100-2221-1-1−i−iii2i2i−2i−2i003-300−3i3i000000002-22-2−2i2i−2i2i00000000-11-11i−ii−i000000000000000000
χ6644-4-4−4i−4i4i4i-2100-2221-1-1−i−iii2i2i−2i−2i003-300−3i3i00000000-22-222i−2i2i−2i000000001-11-1−ii−ii000000000000000000
χ6744-4-4−4i−4i4i4i-2100-2221-1-1−i−iii2i2i−2i−2i00-33003i−3i000000002-2-22−2i2i2i−2i00000000-111-1i−i−ii000000000000000000
χ6844-4-4−4i−4i4i4i-2100-2221-1-1−i−iii2i2i−2i−2i00-33003i−3i00000000-222-22i−2i−2i2i000000001-1-11−iii−i000000000000000000
χ694-4-444-4-441-200-1-1122-2-222-21-1-113i−3i003i−3i0000000000000000002-22-22i−2i2i−2i00000000-11-11−ii−ii0000000000
χ704-4-444-4-441-200-1-1122-2-222-21-1-113i−3i003i−3i000000000000000000-22-22−2i2i−2i2i000000001-11-1i−ii−i0000000000
χ714-4-444-4-441-200-1-1122-2-222-21-1-11−3i3i00−3i3i0000000000000000002-22-2−2i2i−2i2i00000000-11-11i−ii−i0000000000
χ724-4-444-4-441-200-1-1122-2-222-21-1-11−3i3i00−3i3i000000000000000000-22-222i−2i2i−2i000000001-11-1−ii−ii0000000000
χ734-4-44-444-41-200-1-1122-22-2-22-111-13i−3i00−3i3i0000000000000000002i−2i−2i2i-222-200000000−iii−i1-1-110000000000
χ744-4-44-444-41-200-1-1122-22-2-22-111-13i−3i00−3i3i000000000000000000−2i2i2i−2i2-2-2200000000i−i−ii-111-10000000000
χ754-4-44-444-41-200-1-1122-22-2-22-111-1−3i3i003i−3i0000000000000000002i−2i−2i2i2-2-2200000000−iii−i-111-10000000000
χ764-4-44-444-41-200-1-1122-22-2-22-111-1−3i3i003i−3i000000000000000000−2i2i2i−2i-222-200000000i−i−ii1-1-110000000000
χ7788-8-88i8i−8i−8i2-4002-2-2-444−4i−4i4i4i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000
χ7888-8-8−8i−8i8i8i2-4002-2-2-4444i4i−4i−4i−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000
χ798-88-88i−8i8i−8i2-400-22-24-44−4i4i−4i4i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000
χ808-88-88i−8i8i−8i-42004-44-22-22i−2i2i−2i−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000
χ818-88-8−8i8i−8i8i2-400-22-24-444i−4i4i−4i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000
χ828-88-8−8i8i−8i8i-42004-44-22-2−2i2i−2i2i4i−4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ838-8-888-8-88-420044-4-2-222-2-22-444-40000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-8-420044-4-2-22-222-24-4-440000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.