Finite Group Databasebeta

← Group #11722924

Character table — Group #11722924

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222444444444444666666666666668888999912121212121212121212121212121212121212121818181818181818363636365454
order122233366666666633366666666622224466661212121236664444666666666666661212121212124444121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111-1-1111111111111111111-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1-111111-1-1-1-1-11-11111-111-1-1-1-1-11-11-1i−i11-1-1ii−i−i11-1-1ii−i−i1-11-11-111-1-111-1-1i−iii−i−i1-1i−iii−i−i1-1i−ii−i
χ1011-1-111111-1-1-1-1-11-11111-111-1-1-1-1-11-11-1−ii11-1-1−i−iii11-1-1−i−iii1-11-11-111-1-111-1-1−ii−i−iii1-1−ii−i−iii1-1−ii−ii
χ1111-1-111111-1-1-1-1-11-11111-111-1-1-1-1-11-1-11i−i11-1-1ii−i−i11-1-1ii−i−i-111-1-1111-1-1-1-111i−iii−i−i-11−iiii−i−i-11−ii−ii
χ1211-1-111111-1-1-1-1-11-11111-111-1-1-1-1-11-1-11−ii11-1-1−i−iii11-1-1−i−iii-111-1-1111-1-1-1-111−ii−i−iii-11i−i−i−iii-11i−ii−i
χ1311-1-111111-1-1-1-1-11-11111-111-1-1-1-1-1-111-1i−i-1-111ii−i−i11-1-1−i−iii1-1-111-1-1-11111-1-1i−iii−i−i-11i−i−i−iii-11i−i−ii
χ1411-1-111111-1-1-1-1-11-11111-111-1-1-1-1-1-111-1−ii-1-111−i−iii11-1-1ii−i−i1-1-111-1-1-11111-1-1−ii−i−iii-11−iiii−i−i-11−iii−i
χ1511-1-111111-1-1-1-1-11-11111-111-1-1-1-1-1-11-11i−i-1-111ii−i−i11-1-1−i−iii-11-11-11-1-111-1-111i−iii−i−i1-1−ii−i−iii1-1−iii−i
χ1611-1-111111-1-1-1-1-11-11111-111-1-1-1-1-1-11-11−ii-1-111−i−iii11-1-1ii−i−i-11-11-11-1-111-1-111−ii−i−iii1-1i−iii−i−i1-1i−i−ii
χ17222222-1222-1-122-122-1-122-1-1-1-1-1-1222220022220000-1-1-1-1000022-1-1-1-1-1-1-1-1-1-1-1-100000022000000-1-10000
χ18222222-1222-1-122-122-1-122-1-1-1-1-1-1222-2-20022220000-1-1-1-10000-2-2-1-111-1-1-1-11111000000-2-2000000110000
χ19222222-1222-1-122-122-1-122-1-1-1-1-1-12-2-22200-2-2-2-20000-1-1-1-100002211-1-11111-1-1-1-1000000-2-2000000110000
χ20222222-1222-1-122-122-1-122-1-1-1-1-1-12-2-2-2-200-2-2-2-20000-1-1-1-10000-2-211111111111100000022000000-1-10000
χ2122222-122-1222-1-122-12-1-1-12-122-1-1-100222200002222-1-1-1-10000-1-100220000-1-1-1-1-1-1-1-1-1-10022000000-1-100
χ2222222-122-1222-1-122-12-1-1-12-122-1-1-10022-2-20000-2-2-2-2-1-1-1-10000-1-100220000-1-1-1-111111100-2-20000001100
χ2322222-122-1222-1-122-12-1-1-12-122-1-1-100-2-22200002222-1-1-1-100001100-2-200001111-1-1-1-1-1-100-2-20000001100
χ2422222-122-1222-1-122-12-1-1-12-122-1-1-100-2-2-2-20000-2-2-2-2-1-1-1-100001100-2-2000011111111110022000000-1-100
χ252222-122-12-122222-1-1-12-1-1-12-1-122-1220022-1-1-1-1-1-1-1-1-1-1-1-12222002200-1-1-1-1000022-1-1-1-10000-1-1-1-1000000
χ262222-122-12-122222-1-1-12-1-1-12-1-122-12200-2-2-1-1-1-11111-1-1-1-1-2-2-2-2002200-1-1-1-10000-2-2111100001111000000
χ272222-122-12-122222-1-1-12-1-1-12-1-122-1-2-200221111-1-1-1-1-1-1-1-1-2-2-2-200-2-2001111000022-1-1-1-100001111000000
χ282222-122-12-122222-1-1-12-1-1-12-1-122-1-2-200-2-211111111-1-1-1-1222200-2-20011110000-2-211110000-1-1-1-1000000
χ2922-2-222-122-211-2-2-1-22-1-12-2-1-11111-22-22-20022-2-20000-1-11100002-2-11-11-1-111-1-1110000002-2000000-110000
χ3022-2-222-122-211-2-2-1-22-1-12-2-1-11111-22-2-220022-2-20000-1-1110000-22-111-1-1-11111-1-1000000-220000001-10000
χ3122-2-222-122-211-2-2-1-22-1-12-2-1-11111-2-222-200-2-2220000-1-11100002-21-1-1111-1-1-1-111000000-220000001-10000
χ3222-2-222-122-211-2-2-1-22-1-12-2-1-11111-2-22-2200-2-2220000-1-1110000-221-11-111-1-111-1-10000002-2000000-110000
χ3322-2-22-122-1-2-2-2112-2-12-1-112-1-2-2111002-22i−2i00002i2i−2i−2i-1-1110000-11002-20000-1-111−ii−i−iii002i−2i000000−ii00
χ3422-2-22-122-1-2-2-2112-2-12-1-112-1-2-2111002-2−2i2i0000−2i−2i2i2i-1-1110000-11002-20000-1-111i−iii−i−i00−2i2i000000i−i00
χ3522-2-22-122-1-2-2-2112-2-12-1-112-1-2-211100-222i−2i00002i2i−2i−2i-1-11100001-100-22000011-1-1−ii−i−iii00−2i2i000000i−i00
χ3622-2-22-122-1-2-2-2112-2-12-1-112-1-2-211100-22−2i2i0000−2i−2i2i2i-1-11100001-100-22000011-1-1i−iii−i−i002i−2i000000−ii00
χ3722-2-2-122-121-2-2-2-221-1-12-11-1211-2-212-2002i−2i-1-111−i−iii-1-1112i2i−2i−2i002-200-1-11100002i−2i−i−iii0000−i−iii000000
χ3822-2-2-122-121-2-2-2-221-1-12-11-1211-2-212-200−2i2i-1-111ii−i−i-1-111−2i−2i2i2i002-200-1-1110000−2i2iii−i−i0000ii−i−i000000
χ3922-2-2-122-121-2-2-2-221-1-12-11-1211-2-21-22002i−2i11-1-1−i−iii-1-111−2i−2i2i2i00-220011-1-100002i−2i−i−iii0000ii−i−i000000
χ4022-2-2-122-121-2-2-2-221-1-12-11-1211-2-21-2200−2i2i11-1-1ii−i−i-1-1112i2i−2i−2i00-220011-1-10000−2i2iii−i−i0000−i−iii000000
χ412-22-2222-2-222-2-22-2-2222-22-2-22-22-2-2000000000000002-22-22i−2i2i−2i0000000000000000000000002i−2i2i−2i000000
χ422-22-2222-2-222-2-22-2-2222-22-2-22-22-2-2000000000000002-22-2−2i2i−2i2i000000000000000000000000−2i2i−2i2i000000
χ432-22-2-1221-2-12-2-22-21-1-121-11-2-112-21000000−i3i3−i3i33−33−3-11-112i−2i2i−2i000000−i3i3−i3i30000003−33−30000−ii−ii000000
χ442-22-2-1221-2-12-2-22-21-1-121-11-2-112-21000000−i3i3−i3i3−33−33-11-11−2i2i−2i2i000000−i3i3−i3i3000000−33−330000i−ii−i000000
χ452-22-2-1221-2-12-2-22-21-1-121-11-2-112-21000000i3−i3i3−i33−33−3-11-11−2i2i−2i2i000000i3−i3i3−i30000003−33−30000i−ii−i000000
χ462-22-2-1221-2-12-2-22-21-1-121-11-2-112-21000000i3−i3i3−i3−33−33-11-112i−2i2i−2i000000i3−i3i3−i3000000−33−330000−ii−ii000000
χ472-2-22222-2-2-2-222-2-22222-2-2-2-2-22-222000000000000002-2-222-2-220000000000000000000000002-2-22000000
χ482-2-22222-2-2-2-222-2-22222-2-2-2-2-22-222000000000000002-2-22-222-2000000000000000000000000-222-2000000
χ492-2-22-1221-21-222-2-2-1-1-12111-21-1-22-1000000−i3i3i3−i3−i3i3i3−i3-111-12-2-22000000−i3i3i3−i3000000−i3i3i3−i30000-111-1000000
χ502-2-22-1221-21-222-2-2-1-1-12111-21-1-22-1000000−i3i3i3−i3i3−i3−i3i3-111-1-222-2000000−i3i3i3−i3000000i3−i3−i3i300001-1-11000000
χ512-2-22-1221-21-222-2-2-1-1-12111-21-1-22-1000000i3−i3−i3i3−i3i3i3−i3-111-1-222-2000000i3−i3−i3i3000000−i3i3i3−i300001-1-11000000
χ522-2-22-1221-21-222-2-2-1-1-12111-21-1-22-1000000i3−i3−i3i3i3−i3−i3i3-111-12-2-22000000i3−i3−i3i3000000i3−i3−i3i30000-111-1000000
χ5344444-2-24-24-2-2-2-2-24-2-21-2-2-21-2-211-20044000000000011110000-2-200-2-20000111100000000000000000000
χ5444444-2-24-24-2-2-2-2-24-2-21-2-2-21-2-211-200-4-40000000000111100002200220000-1-1-1-100000000000000000000
χ554444-24-2-24-2-2-244-2-2-21-2-2-21-211-2-2-2440000-2-2-2-200001111000000-2-2001111000000000000000000000000
χ564444-24-2-24-2-2-244-2-2-21-2-2-21-211-2-2-2-4-400002222000011110000002200-1-1-1-1000000000000000000000000
χ574444-2-24-2-2-244-2-24-21-2-211-2-2-2-2-2-210000440000-2-2-2-21111000000000000000000-2-2111100000000000000
χ584444-2-24-2-2-244-2-24-21-2-211-2-2-2-2-2-210000-4-400002222111100000000000000000022-1-1-1-100000000000000
χ5944-4-44-2-24-2-42222-2-4-2-21-22-2122-1-12004-4000000000011-1-10000-2200-22000011-1-100000000000000000000
χ6044-4-44-2-24-2-42222-2-4-2-21-22-2122-1-1200-44000000000011-1-100002-2002-20000-1-11100000000000000000000
χ6144-4-4-24-2-24222-4-4-22-21-2-221-2-1-12224-40000-2-222000011-1-1000000-220011-1-1000000000000000000000000
χ6244-4-4-24-2-24222-4-4-22-21-2-221-2-1-1222-44000022-2-2000011-1-10000002-200-1-111000000000000000000000000
χ6344-4-4-2-24-2-22-4-422421-2-21-1-2-22222-100004i−4i0000−2i−2i2i2i11-1-1000000000000000000−2i2iii−i−i00000000000000
χ6444-4-4-2-24-2-22-4-422421-2-21-1-2-22222-10000−4i4i00002i2i−2i−2i11-1-10000000000000000002i−2i−i−iii00000000000000
χ654-44-444-2-4-44-22-442-44-2-2-4422-22-22-400000000000000-22-2200000000000000000000000000000000000000
χ664-44-44-24-4244-42-2-4-4-24-22-2-424-4-22200000000000000-22-2200000000000000000000000000000000000000
χ674-44-44-2-2-424-222-22-4-2-212-22-1-221-12000000000000001-11-1000000000000003-33-300000000000000000000
χ684-44-44-2-2-424-222-22-4-2-212-22-1-221-12000000000000001-11-100000000000000-33-3300000000000000000000
χ694-44-4-24-22-4-2-22-4422-21-22-2-121-1-222000000−2i32i3−2i32i300001-11-10000000000i3−i3i3−i3000000000000000000000000
χ704-44-4-24-22-4-2-22-4422-21-22-2-121-1-2220000002i3−2i32i3−2i300001-11-10000000000−i3i3−i3i3000000000000000000000000
χ714-44-4-2-2422-24-42-2-421-2-2-1122-22-22-1000000000023−2323−231-11-100000000000000000000−33−3300000000000000
χ724-44-4-2-2422-24-42-2-421-2-2-1122-22-22-10000000000−2323−23231-11-1000000000000000000003−33−300000000000000
χ734-4-4444-2-4-4-42-24-4244-2-2-4-4222-22-2400000000000000-222-200000000000000000000000000000000000000
χ744-4-444-24-42-4-44-22-44-24-222-42-442-2-200000000000000-222-200000000000000000000000000000000000000
χ754-4-444-2-2-42-42-2-2224-2-21222-12-2-11-2000000000000001-1-11000000000000003-3-3300000000000000000000
χ764-4-444-2-2-42-42-2-2224-2-21222-12-2-11-2000000000000001-1-1100000000000000-333-300000000000000000000
χ774-4-44-24-22-422-24-42-2-21-222-12-112-2-2000000−2i32i32i3−2i300001-1-110000000000i3−i3−i3i3000000000000000000000000
χ784-4-44-24-22-422-24-42-2-21-222-12-112-2-20000002i3−2i3−2i32i300001-1-110000000000−i3i3i3−i3000000000000000000000000
χ794-4-44-2-24222-44-22-4-21-2-2-1-1222-22-210000000000−2i32i32i3−2i31-1-1100000000000000000000i3−i3−i3i300000000000000
χ804-4-44-2-24222-44-22-4-21-2-2-1-1222-22-2100000000002i3−2i3−2i32i31-1-1100000000000000000000−i3i3i3−i300000000000000
χ818888-4-4-4-4-4-4-4-4-4-4-4-422222222222200000000000000-1-1-1-100000000000000000000000000000000000000
χ8288-8-8-4-4-4-4-444444-442222-222-2-2-2-2-200000000000000-1-11100000000000000000000000000000000000000
χ838-88-8-4-4-444-4-444-444222-22-2-22-22-2-200000000000000-11-1100000000000000000000000000000000000000
χ848-8-88-4-4-44444-4-444-4222-2-2-2-2-22-22200000000000000-111-100000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).