Finite Group Databasebeta

← Group #72285762

Character table — Group #72285762

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1124448888161616161616161616323232323232323232323232323232323232646464646464646464646464128128128128
order12222222442224444442244444444888888884444444444448888
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-11-1-11111111111111-1-1-1-11-1-11111-1-1-1-1
χ411111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-11111
χ51111111111111111111-11-1-11-111-1-111111111-11-11-1-11-1-1-1-1-111-1-1
χ61111111111111111111-11-1-11-111-1-1-1-1-1-1-1-1-1-1-11-11-1-11-11111-1-111
χ71111111111111111111-1-11-1-1111-1-111111111-1-11-11-1-11-1-1-1-1-1-111
χ81111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111111-1-1
χ911111111-1-11-1-11-1-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1111-1-1ii−i−ii−ii−i
χ1011111111-1-11-1-11-1-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1111-1-1−i−iii−ii−ii
χ1111111111-1-11-1-11-1-1-1-1-11-1-11-1-111-1-1iiii−i−i−i−i-111-1-1111ii−i−i−ii−ii
χ1211111111-1-11-1-11-1-1-1-1-11-1-11-1-111-1-1−i−i−i−iiiii-111-1-1111−i−iiii−ii−i
χ1311111111-1-11-1-11-1-1-1-1-1-11-1-11-11111iiii−i−i−i−i1-111-1-1-11−i−iiii−i−ii
χ1411111111-1-11-1-11-1-1-1-1-1-11-1-11-11111−i−i−i−iiiii1-111-1-1-11ii−i−i−iii−i
χ1511111111-1-11-1-11-1-1-1-1-1-1-11-1-111111iiii−i−i−i−i11-1-11-11-1−i−iii−iii−i
χ1611111111-1-11-1-11-1-1-1-1-1-1-11-1-111111−i−i−i−iiiii11-1-11-11-1ii−i−ii−i−ii
χ17222222222222222-2-2-2-2200200-2-2-2-20000000020000-20000000000
χ18222222222222222-2-2-2-2-200-200-2-22200000000-2000020000000000
χ192222222222-22-2-2-222-2-20020022-200000000000020-200-200000000
χ202222222222-22-2-2-222-2-200-200-22-2000000000000-20200200000000
χ212222222222-22-2-2-2-2-222020020-220000000000020-200-2000000000
χ222222222222-22-2-2-2-2-2220-200-20-2200000000000-202002000000000
χ2322222222-2-22-2-22-22222200200-2-22200000000-20000-20000000000
χ2422222222-2-22-2-22-22222-200-200-2-2-2-2000000002000020000000000
χ2522222222-2-2-2-22-2222-2-2020020-2200000000000-20-2002000000000
χ2622222222-2-2-2-22-2222-2-20-200-20-220000000000020200-2000000000
χ2722222222-2-2-2-22-22-2-2220020022-2000000000000-20-200200000000
χ2822222222-2-2-2-22-22-2-22200-200-22-200000000000020200-200000000
χ292222-2-22-200-200202i−2i2i−2i200-200002i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000001+i−1−i1−i−1+i0000
χ302222-2-22-200-200202i−2i2i−2i200-200002i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−1−i1+i−1+i1−i0000
χ312222-2-22-200-200202i−2i2i−2i-20020000−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−1−i1+i−1+i1−i0000
χ322222-2-22-200-200202i−2i2i−2i-20020000−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000001+i−1−i1−i−1+i0000
χ332222-2-22-200-20020−2i2i−2i2i200-20000−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000001−i−1+i1+i−1−i0000
χ342222-2-22-200-20020−2i2i−2i2i200-20000−2i2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−1+i1−i−1−i1+i0000
χ352222-2-22-200-20020−2i2i−2i2i-200200002i−2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−1+i1−i−1−i1+i0000
χ362222-2-22-200-20020−2i2i−2i2i-200200002i−2i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000001−i−1+i1+i−1−i0000
χ37444444-4-4440-4000000000000000002-22-22-22-20000000000000000
χ38444444-4-4440-400000000000000000-22-22-22-220000000000000000
χ39444444-4-4-4-404000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ40444444-4-4-4-40400000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ414444-4-44-400400-404i−4i−4i4i0000000000000000000000000000000000
χ424444-4-44-400400-40−4i4i4i−4i0000000000000000000000000000000000
χ434444-4-4-44000040-4000000000000002-2-222-2-220000000000000000
χ444444-4-4-44000040-400000000000000-222-2-222-20000000000000000
χ454444-4-4-440000-404000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ464444-4-4-440000-40400000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ47888-88-8000000000000000400-40000000000000000000000000000
χ48888-88-8000000000000000-40040000000000000000000000000000
χ49888-8-8800000000000000400-400000000000000000000000000000
χ50888-8-8800000000000000-400400000000000000000000000000000
χ511616-16000008-80000000000000000000000000000000000000000000
χ521616-1600000-880000000000000000000000000000000000000000000
χ5332-32000000000000000000000000000000000000000000000000000

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