Finite Group Databasebeta

← Group #72231793

Character table — Group #72231793

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222224444444444488888888888888888881616161616161616161616242424242424242432323232323232323232323248484848484848489696
order12222362222224466622224446666666666121244661212121212121222224444444412121212121212124444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-111-1-11111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1
χ6111111111111111111-1-111-1-11111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111
χ7111111111111111111-1-111-1-11111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111
χ8111111111111111111-1-111-1-11111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1111111-1-1
χ911111111111-1-11111111-1-111-11111-1-1-1-1-1-111-1-111-111-1-1-1-111111111i−ii−iii−i−iii−i−i-1-1-1-1ii−i−ii−i
χ1011111111111-1-11111111-1-111-11111-1-1-1-1-1-111-1-111-111-1-1-1-111111111−ii−ii−i−iii−i−iii-1-1-1-1−i−iii−ii
χ1111111111111-1-11111111-1-111-11111-1-1-1-1-1-111-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iii−i−iii−i−i1111−i−iii−ii
χ1211111111111-1-11111111-1-111-11111-1-1-1-1-1-111-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−iii−i−iii1111ii−i−ii−i
χ1311111111111-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111111-1-111-1-1i−i−iiii−i−i−i−iii-1-111ii−i−i−ii
χ1411111111111-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1111111-1-111-1-1−iii−i−i−iiiii−i−i-1-111−i−iiii−i
χ1511111111111-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-111i−i−iiii−i−i−i−iii11-1-1−i−iiii−i
χ1611111111111-1-111111-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-111−iii−i−i−iiiii−i−i11-1-1ii−i−i−ii
χ17222222222-2-222-2-2222002-200-222-2-22222-2-2-2-20000-2000000002-2002-2000000000000002-2000000
χ18222222222-2-222-2-2222002-200-222-2-22222-2-2-2-20000-200000000-2200-2200000000000000-22000000
χ19222222222-2-2-2-2-2-222200-2200222-2-2-2-2-2-222-2-200002000000002-2002-200000000000000-22000000
χ20222222222-2-2-2-2-2-222200-2200222-2-2-2-2-2-222-2-20000200000000-2200-22000000000000002-2000000
χ212222222-2-22222-2-222200-2200-2-2-22222-2-222-2-20000-20000002-2002-2000000000000002-200000000
χ222222222-2-22222-2-222200-2200-2-2-22222-2-222-2-20000-2000000-2200-2200000000000000-2200000000
χ232222222-2-222-2-2-2-2222002-2002-2-222-2-222-2-2-2-2000020000002-2002-200000000000000-2200000000
χ242222222-2-222-2-2-2-2222002-2002-2-222-2-222-2-2-2-200002000000-2200-22000000000000002-200000000
χ252222222-2-2-2-222222222-2-2-22-22-2-2-2-222-2-2-2-2222-22-222-222-2-2000000000000000000000000000000
χ262222222-2-2-2-22222222-22-2-2-222-2-2-2-222-2-2-2-222-22-222-22-2-222000000000000000000000000000000
χ272222222-2-2-2-2-2-2222222-2222-2-2-2-2-2-2-2-2222222-222-2-22-2-2-222000000000000000000000000000000
χ282222222-2-2-2-2-2-222222-2222-22-2-2-2-2-2-2-22222222-2-22-2-2222-2-2000000000000000000000000000000
χ2922222-1-122222222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-10000000000
χ3022222-1-122222222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-100000000-2-2-2-2111111110000000000
χ3122222-1-122222222-1-1-1-2-222-2-22-1-1-1-1-1-1-1-1-1-1-1-1-2-211-11111110000000022-2-2-1-1-1-111110000000000
χ3222222-1-122222222-1-1-1-2-222-2-22-1-1-1-1-1-1-1-1-1-1-1-1-2-211-111111100000000-2-2221111-1-1-1-10000000000
χ3322222-1-12222-2-222-1-1-122-2-222-2-1-1-1-1111111-1-1-2-2-1-11-1-11111000000002i−2i2i−2i−i−iii−i−iii0000000000
χ3422222-1-12222-2-222-1-1-122-2-222-2-1-1-1-1111111-1-1-2-2-1-11-1-1111100000000−2i2i−2i2iii−i−iii−i−i0000000000
χ3522222-1-12222-2-222-1-1-1-2-2-2-2-2-2-2-1-1-1-1111111-1-12211111-1-1-1-1000000002i−2i−2i2i−i−iiiii−i−i0000000000
χ3622222-1-12222-2-222-1-1-1-2-2-2-2-2-2-2-1-1-1-1111111-1-12211111-1-1-1-100000000−2i2i2i−2iii−i−i−i−iii0000000000
χ3722222-1-1-2-2-2-22222-1-1-12-2-2-22-221111-1-11111-1-12-2-11-1-11-1-1110000000000003−33−33−33−30000000000
χ3822222-1-1-2-2-2-22222-1-1-12-2-2-22-221111-1-11111-1-12-2-11-1-11-1-111000000000000−33−33−33−330000000000
χ3922222-1-1-2-2-2-22222-1-1-1-22-2-2-2221111-1-11111-1-1-221-1-11-111-1-10000000000003−33−3−33−330000000000
χ4022222-1-1-2-2-2-22222-1-1-1-22-2-2-2221111-1-11111-1-1-221-1-11-111-1-1000000000000−33−333−33−30000000000
χ4122222-1-1-2-2-2-2-2-222-1-1-12-2222-2-2111111-1-1-1-1-1-1-22-111-1111-1-1000000000000−i3i3i3−i3−i3i3i3−i30000000000
χ4222222-1-1-2-2-2-2-2-222-1-1-12-2222-2-2111111-1-1-1-1-1-1-22-111-1111-1-1000000000000i3−i3−i3i3i3−i3−i3i30000000000
χ4322222-1-1-2-2-2-2-2-222-1-1-1-2222-22-2111111-1-1-1-1-1-12-21-111-1-1-111000000000000−i3i3i3−i3i3−i3−i3i30000000000
χ4422222-1-1-2-2-2-2-2-222-1-1-1-2222-22-2111111-1-1-1-1-1-12-21-111-1-1-111000000000000i3−i3−i3i3−i3i3i3−i30000000000
χ4544444-2-244-4-444-4-4-2-2-2004-400-4-2-222-2-2-2-2222200002000000000000000000000000000000000000
χ4644444-2-244-4-4-4-4-4-4-2-2-200-44004-2-2222222-2-2220000-2000000000000000000000000000000000000
χ4744444-2-2-4-44444-4-4-2-2-200-4400-422-2-2-2-222-2-22200002000000000000000000000000000000000000
χ4844444-2-2-4-444-4-4-4-4-2-2-2004-400422-2-222-2-222220000-2000000000000000000000000000000000000
χ49444-4-4440000004-4-4-4404000-4000000000004-4000400-40000000000000000000000000000000000
χ50444-4-4440000004-4-4-440-40004000000000004-4000-40040000000000000000000000000000000000
χ51444-4-444000000-44-4-444000-4000000000000-4400400-400000000000000000000000000000000000
χ52444-4-444000000-44-4-44-40004000000000000-4400-400400000000000000000000000000000000000
χ53444-4-4-2-20000004-422-204000-40000000−2i32i3−2i32i3-22000-2002−2i32i300000000000000000000000000000000
χ54444-4-4-2-20000004-422-204000-400000002i3−2i32i3−2i3-22000-20022i3−2i300000000000000000000000000000000
χ55444-4-4-2-20000004-422-20-400040000000−2i32i3−2i32i3-22000200-22i3−2i300000000000000000000000000000000
χ56444-4-4-2-20000004-422-20-4000400000002i3−2i32i3−2i3-22000200-2−2i32i300000000000000000000000000000000
χ57444-4-4-2-2000000-4422-24000-400000000−2i32i32i3−2i32-200-2002000−2i32i3000000000000000000000000000000
χ58444-4-4-2-2000000-4422-24000-4000000002i3−2i3−2i32i32-200-20020002i3−2i3000000000000000000000000000000
χ59444-4-4-2-2000000-4422-2-4000400000000−2i32i32i3−2i32-200200-20002i3−2i3000000000000000000000000000000
χ60444-4-4-2-2000000-4422-2-40004000000002i3−2i3−2i32i32-200200-2000−2i32i3000000000000000000000000000000
χ6144-44-444004-400004-4-40000000004-4000000000000000000004000-4000000000000000000000000
χ6244-44-444004-400004-4-40000000004-400000000000000000000-40004000000000000000000000000
χ6344-44-44400-4400004-4-4000000000-4400000000000000000004000-40000000000000000000000000
χ6444-44-44400-4400004-4-4000000000-440000000000000000000-400040000000000000000000000000
χ6544-4-44444-4000000-44-400000004-40000000000000000000000004000-40000000000000000000000
χ6644-4-44444-4000000-44-400000004-4000000000000000000000000-400040000000000000000000000
χ6744-4-4444-44000000-44-40000000-44000000000000000000000004000-400000000000000000000000
χ6844-4-4444-44000000-44-40000000-4400000000000000000000000-4000400000000000000000000000
χ6988-88-8-4-4008-80000-444000000000-440000000000000000000000000000000000000000000000000
χ7088-88-8-4-400-880000-4440000000004-40000000000000000000000000000000000000000000000000
χ7188-8-88-4-48-80000004-440000000-44000000000000000000000000000000000000000000000000000
χ7288-8-88-4-4-880000004-4400000004-4000000000000000000000000000000000000000000000000000
χ738-80008-800004-400000000000000004-4000000000000000000000000000000000000000002i−2i2i−2i00
χ748-80008-800004-400000000000000004-400000000000000000000000000000000000000000−2i2i−2i2i00
χ758-80008-80000-440000000000000000-44000000000000000000000000000000000000000002-2-2200
χ768-80008-80000-440000000000000000-4400000000000000000000000000000000000000000-222-200
χ7716-16000-8800008-80000000000000000-4400000000000000000000000000000000000000000000000
χ7816-16000-880000-8800000000000000004-400000000000000000000000000000000000000000000000

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