Finite Group Databasebeta

← Group #11775879

Character table — Group #11775879

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222244444444444444466666666668888888888888121212121212121212121216161616161624242424242424242424242424242424363636367272
order1222334444666666346661212121212121212121222444412121212246612121212121212121246688881212121266612121224668812122424242424242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-11-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111-1-1-1-11-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-11111-1-1-1-1111111-1-1-1-111-1-111111111-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ9111111-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-11111111-1111-1-1-1-1-1-111-111ii−i−i-1-1-1-1111-1-1-1-11-1-1i−i11ii−i−iii−i−iii−i−ii−i
χ10111111-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-11111111-1111-1-1-1-1-1-111-111−i−iii-1-1-1-1111-1-1-1-11-1-1−ii11−i−iii−i−iii−i−iii−ii
χ11111111-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-1111111-11-1-1111-1-1-1-111-111ii−i−i-1-1-1-1-1-1-11111-111−ii-1-1ii−i−i−i−iiiii−i−i−ii
χ12111111-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-1111111-11-1-1111-1-1-1-111-111−i−iii-1-1-1-1-1-1-11111-111i−i-1-1−i−iiiii−i−i−i−iiii−i
χ13111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11-1111-1-1-1-1-1-1111-1-1ii−i−i1111111-1-1-11-111i−i-1-1ii−i−iii−i−i−i−iii−ii
χ14111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11-1111-1-1-1-1-1-1111-1-1−i−iii1111111-1-1-11-111−ii-1-1−i−iii−i−iiiii−i−ii−i
χ15111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1111-1-1-1-1111-1-1ii−i−i1111-1-1-1111-11-1-1−ii11ii−i−i−i−iii−i−iiii−i
χ16111111-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-1-1111-1-1-1-1111-1-1−i−iii1111-1-1-1111-11-1-1i−i11−i−iiiii−i−iii−i−i−ii
χ1722222222-2-22222222-222222-2-2-2-222-2-22222-2-2-2-2-2-20000-20022-2-2-2-2-222000022-2-20000000000000000000000000000
χ1822222222-2-22222222-222222-2-2-2-222-2-2-2-2-2-22222220000-20022-2-2-2-22-2-20000-2-2220000000000000000000000000000
χ19222222-2-2222222222-2222-2-222-2-2-2-22222-2-2-2-2-2-2-2-20000-200-2-222-2-22220000-2-2220000000000000000000000000000
χ20222222-2-2222222222-2222-2-222-2-2-2-222-2-2222222220000-200-2-222-2-2-2-2-2000022-2-20000000000000000000000000000
χ2122222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-12222222222-1-1-1-122-1-12-1-1-1-1-1-1-1-12-1-10000-1-1-1-12-1-12-1-122-1-100-1-100000000000000
χ2222222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-2-211211-1-1-1-1-1-12-1-10000-1-1-1-1-211-211-2-211001100000000000000
χ2322222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2111122-1-12-1-1-1-1-1-1-1-1-211000011112-1-12-1-1-2-211001100000000000000
χ2422222-12222222-1-1-1-12-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-21111-2-211211-1-1-1-1-1-1-21100001111-211-21122-1-100-1-100000000000000
χ2522222-122-2-2222-1-1-1-1-2-1-1-1-1-1111122-2-22222-2-2111100−i3i3-2−i3i3-1-11111-2-1-10000-1-1110−i3i30−i3i300−i3i300−i3i300000000000000
χ2622222-122-2-2222-1-1-1-1-2-1-1-1-1-1111122-2-22222-2-2111100i3−i3-2i3−i3-1-11111-2-1-10000-1-1110i3−i30i3−i300i3−i300i3−i300000000000000
χ2722222-122-2-2222-1-1-1-1-2-1-1-1-1-1111122-2-2-2-2-2-222-1-1-1-100−i3i3-2−i3i3-1-11111211000011-1-10−i3i30−i3i300i3−i300i3−i300000000000000
χ2822222-122-2-2222-1-1-1-1-2-1-1-1-1-1111122-2-2-2-2-2-222-1-1-1-100i3−i3-2i3−i3-1-11111211000011-1-10i3−i30i3−i300−i3i300−i3i300000000000000
χ2922222-1-2-222222-1-1-1-1-2-1-1-111-1-111-2-22222-2-2-2-2111100−i3i3-2i3−i311-1-1112-1-1000011-1-10−i3i30i3−i300i3−i300−i3i300000000000000
χ3022222-1-2-222222-1-1-1-1-2-1-1-111-1-111-2-22222-2-2-2-2111100i3−i3-2−i3i311-1-1112-1-1000011-1-10i3−i30−i3i300−i3i300i3−i300000000000000
χ3122222-1-2-222222-1-1-1-1-2-1-1-111-1-111-2-222-2-22222-1-1-1-100−i3i3-2i3−i311-1-111-2110000-1-1110−i3i30i3−i300−i3i300i3−i300000000000000
χ3222222-1-2-222222-1-1-1-1-2-1-1-111-1-111-2-222-2-22222-1-1-1-100i3−i3-2−i3i311-1-111-2110000-1-1110i3−i30−i3i300i3−i300−i3i300000000000000
χ3322222-1-2-2-2-2222-1-1-1-12-1-1-11111-1-1-2-2-2-222-2-222-1-1-1-12-2-1-12111111-1-1-2-1-1000011112-1-1-211-221100-1-100000000000000
χ3422222-1-2-2-2-2222-1-1-1-12-1-1-11111-1-1-2-2-2-222-2-222-1-1-1-1-22112-1-11111-1-1-2-1-100001111-2112-1-12-2-1-1001100000000000000
χ3522222-1-2-2-2-2222-1-1-1-12-1-1-11111-1-1-2-2-2-2-2-222-2-211112-2-1-12111111-1-12110000-1-1-1-12-1-1-2112-2-1-1001100000000000000
χ3622222-1-2-2-2-2222-1-1-1-12-1-1-11111-1-1-2-2-2-2-2-222-2-21111-22112-1-11111-1-12110000-1-1-1-1-2112-1-1-221100-1-100000000000000
χ372222-122222-1-1-1222-12-1-1-1222222-1-1-1-100000000002222-122-1-1-1-1-1-100022220000-1-1-1-1-1-100002200-1-1-1-1-1-1-1-1000000
χ382222-122222-1-1-1222-12-1-1-1222222-1-1-1-100000000002222-122-1-1-1-1-1-1000-2-2-2-20000-1-1-1-1-1-10000-2-20011111111000000
χ392222-122222-1-1-1222-12-1-1-1222222-1-1-1-10000000000-2-2-2-2-1-2-2-1-1-1-1-1-1000222200001111110000-2-200-1-1-1-11111000000
χ402222-122222-1-1-1222-12-1-1-1222222-1-1-1-10000000000-2-2-2-2-1-2-2-1-1-1-1-1-1000-2-2-2-20000111111000022001111-1-1-1-1000000
χ412222-12-2-2-2-2-1-1-1222-12-1-1-1-2-2-2-222111100000000002-222-1-2-21111-1-10002i2i−2i−2i0000-1-1-111100002i−2i00−i−iii−i−iii000000
χ422222-12-2-2-2-2-1-1-1222-12-1-1-1-2-2-2-222111100000000002-222-1-2-21111-1-1000−2i−2i2i2i0000-1-1-11110000−2i2i00ii−i−iii−i−i000000
χ432222-12-2-2-2-2-1-1-1222-12-1-1-1-2-2-2-22211110000000000-22-2-2-1221111-1-10002i2i−2i−2i0000111-1-1-10000−2i2i00−i−iiiii−i−i000000
χ442222-12-2-2-2-2-1-1-1222-12-1-1-1-2-2-2-22211110000000000-22-2-2-1221111-1-1000−2i−2i2i2i0000111-1-1-100002i−2i00ii−i−i−i−iii000000
χ4522-2-222002i−2i2-2-22-2-2202-2-2002i−2i00002i−2i002-22i−2i2i2i−2i−2i0000000002i−2i000001+i−1−i1−i−1+i2-200000000000000001+i−1−i1−i−1+i00001−i−1+i1+i−1−i00
χ4622-2-222002i−2i2-2-22-2-2202-2-2002i−2i00002i−2i002-22i−2i2i2i−2i−2i0000000002i−2i00000−1−i1+i−1+i1−i2-20000000000000000−1−i1+i−1+i1−i0000−1+i1−i−1−i1+i00
χ4722-2-222002i−2i2-2-22-2-2202-2-2002i−2i00002i−2i00-22−2i2i−2i−2i2i2i0000000002i−2i000001+i−1−i1−i−1+i-2200000000000000001+i−1−i1−i−1+i0000−1+i1−i−1−i1+i00
χ4822-2-222002i−2i2-2-22-2-2202-2-2002i−2i00002i−2i00-22−2i2i−2i−2i2i2i0000000002i−2i00000−1−i1+i−1+i1−i-220000000000000000−1−i1+i−1+i1−i00001−i−1+i1+i−1−i00
χ4922-2-22200−2i2i2-2-22-2-2202-2-200−2i2i0000−2i2i002-2−2i2i−2i−2i2i2i000000000−2i2i000001−i−1+i1+i−1−i2-200000000000000001−i−1+i1+i−1−i00001+i−1−i1−i−1+i00
χ5022-2-22200−2i2i2-2-22-2-2202-2-200−2i2i0000−2i2i002-2−2i2i−2i−2i2i2i000000000−2i2i00000−1+i1−i−1−i1+i2-20000000000000000−1+i1−i−1−i1+i0000−1−i1+i−1+i1−i00
χ5122-2-22200−2i2i2-2-22-2-2202-2-200−2i2i0000−2i2i00-222i−2i2i2i−2i−2i000000000−2i2i000001−i−1+i1+i−1−i-2200000000000000001−i−1+i1+i−1−i0000−1−i1+i−1+i1−i00
χ5222-2-22200−2i2i2-2-22-2-2202-2-200−2i2i0000−2i2i00-222i−2i2i2i−2i−2i000000000−2i2i00000−1+i1−i−1−i1+i-220000000000000000−1+i1−i−1−i1+i00001+i−1−i1−i−1+i00
χ534444-2444-4-4-2-2-2444-2-4-2-2-244-4-4-4-4-2-22200000000000000200-2-22222000000000000000000000000000000000000000
χ544444-24-4-444-2-2-2444-2-4-2-2-2-4-444-4-422-2-20000000000000020022-2-222000000000000000000000000000000000000000
χ554444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-2-2000000000044-2-2-2-2-211111100000000000-211-2110000000000000000000000
χ564444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-2-20000000000-4-422-222111111000000000002-1-12-1-10000000000000000000000
χ574444-2-244-4-4-2-2-2-2-2-21-4111-2-22222-2-222000000000000−2i32i32−2i32i311-1-1-1-1000000000000i3−i30i3−i30000000000000000000000
χ584444-2-244-4-4-2-2-2-2-2-21-4111-2-22222-2-2220000000000002i3−2i322i3−2i311-1-1-1-1000000000000−i3i30−i3i30000000000000000000000
χ594444-2-2-4-444-2-2-2-2-2-21-411122-2-22222-2-2000000000000−2i32i322i3−2i3-1-111-1-1000000000000i3−i30−i3i30000000000000000000000
χ604444-2-2-4-444-2-2-2-2-2-21-411122-2-22222-2-20000000000002i3−2i32−2i32i3-1-111-1-1000000000000−i3i30i3−i30000000000000000000000
χ614444-2-2-4-4-4-4-2-2-2-2-2-2141112222-2-2222200000000004-4-2-2-222-1-1-1-11100000000000-2112-1-10000000000000000000000
χ624444-2-2-4-4-4-4-2-2-2-2-2-2141112222-2-222220000000000-4422-2-2-2-1-1-1-111000000000002-1-1-2110000000000000000000000
χ6344-4-44-2004i−4i4-4-4-222-20-22200−2i2i00004i−4i004-44i−4i−2i−2i2i2i000000000−2i2i000000000-22000000000000000000000000000000
χ6444-4-44-2004i−4i4-4-4-222-20-22200−2i2i00004i−4i00-44−4i4i2i2i−2i−2i000000000−2i2i0000000002-2000000000000000000000000000000
χ6544-4-44-200−4i4i4-4-4-222-20-222002i−2i0000−4i4i004-4−4i4i2i2i−2i−2i0000000002i−2i000000000-22000000000000000000000000000000
χ6644-4-44-200−4i4i4-4-4-222-20-222002i−2i0000−4i4i00-444i−4i−2i−2i2i2i0000000002i−2i0000000002-2000000000000000000000000000000
χ6744-4-4-24004i−4i-2224-4-4-20-222004i−4i0000−2i2i0000000000000000000−2i2i000002+2i−2−2i2−2i−2+2i000000000000000000−1−i1+i−1+i1−i0000000000
χ6844-4-4-24004i−4i-2224-4-4-20-222004i−4i0000−2i2i0000000000000000000−2i2i00000−2−2i2+2i−2+2i2−2i0000000000000000001+i−1−i1−i−1+i0000000000
χ6944-4-4-2400−4i4i-2224-4-4-20-22200−4i4i00002i−2i00000000000000000002i−2i000002−2i−2+2i2+2i−2−2i000000000000000000−1+i1−i−1−i1+i0000000000
χ7044-4-4-2400−4i4i-2224-4-4-20-22200−4i4i00002i−2i00000000000000000002i−2i00000−2+2i2−2i−2−2i2+2i0000000000000000001−i−1+i1+i−1−i0000000000
χ714-44-4444i−4i00-44-4-44-440-44-44i−4i00004i−4i00000000000000000004i−4i0000000000000000000000000000000000000000000
χ724-44-444−4i4i00-44-4-44-440-44-4−4i4i0000−4i4i0000000000000000000−4i4i0000000000000000000000000000000000000000000
χ734-44-44-24i−4i00-44-42-22-202-22−2i2i00004i−4i0000000023−2323−230000000−2i2i0000000000000−2i32i30000000000000000000000000000
χ744-44-44-24i−4i00-44-42-22-202-22−2i2i00004i−4i00000000−2323−23230000000−2i2i00000000000002i3−2i30000000000000000000000000000
χ754-44-44-2−4i4i00-44-42-22-202-222i−2i0000−4i4i0000000023−2323−2300000002i−2i00000000000002i3−2i30000000000000000000000000000
χ764-44-44-2−4i4i00-44-42-22-202-222i−2i0000−4i4i00000000−2323−232300000002i−2i0000000000000−2i32i30000000000000000000000000000
χ774-44-4-244i−4i002-22-44-4-202-224i−4i0000−2i2i0000000000000000000−2i2i000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000
χ784-44-4-244i−4i002-22-44-4-202-224i−4i0000−2i2i0000000000000000000−2i2i000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000
χ794-44-4-24−4i4i002-22-44-4-202-22−4i4i00002i−2i00000000000000000002i−2i000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000
χ804-44-4-24−4i4i002-22-44-4-202-22−4i4i00002i−2i00000000000000000002i−2i000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000
χ814-4-44440000-4-44-4-4440-4-4400000000004-400000000000000000000004-4000000000000000000000000000000000000
χ824-4-44440000-4-44-4-4440-4-440000000000-440000000000000000000000-44000000000000000000000000000000000000
χ834-4-444-20000-4-4422-2-2022-20000−2i32i300004-40000−2i32i32i3−2i300000000000−2i32i30-22000000000000000000000000000000000000
χ844-4-444-20000-4-4422-2-2022-20000−2i32i30000-4400002i3−2i3−2i32i300000000000−2i32i302-2000000000000000000000000000000000000
χ854-4-444-20000-4-4422-2-2022-200002i3−2i300004-400002i3−2i3−2i32i3000000000002i3−2i30-22000000000000000000000000000000000000
χ864-4-444-20000-4-4422-2-2022-200002i3−2i30000-440000−2i32i32i3−2i3000000000002i3−2i302-2000000000000000000000000000000000000
χ8788-8-8-4-4008i−8i-444-444202-2-200−4i4i0000−4i4i00000000000000000002i−2i00000000000000000000000000000000000000000
χ8888-8-8-4-400−8i8i-444-444202-2-2004i−4i00004i−4i0000000000000000000−2i2i00000000000000000000000000000000000000000
χ898-88-8-4-48i−8i004-444-4420-22-2−4i4i0000−4i4i00000000000000000002i−2i0000000000000000000000000000000000000000000
χ908-88-8-4-4−8i8i004-444-4420-22-24i−4i00004i−4i0000000000000000000−2i2i0000000000000000000000000000000000000000000
χ918-8-88-48000044-4-8-88-4044-4000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88-4-4000044-444-420-2-220000−4i34i300000000000000000000000002i3−2i3000000000000000000000000000000000000000
χ938-8-88-4-4000044-444-420-2-2200004i3−4i30000000000000000000000000−2i32i3000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.