Finite Group Databasebeta

← Group #72325868

Character table — Group #72325868

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122244444488881616161616161616161616161616161616163232323232323232323232323232323232646464646464128128128128128128
order12222222222224422222244444444444444444444444444444444444888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111
χ51111111111111111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1ii−i−ii−iii−i−i
χ61111111111111111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1−i−iii−ii−i−iii
χ71111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1ii−i−ii−i−i−iii
χ81111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1−i−iii−iiii−i−i
χ911111111111111111-1-11111-1-111111111-1-11111-1-1-1-1-1-1-1-1111-1-11111-1-11-11-1
χ1011111111111111111-1-11111-1-111111111-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-11-11
χ1111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11111-1-1-11-11
χ1211111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1111-11-1
χ1311111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111ii−i−i−iii−i−ii
χ1411111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111−i−iiii−i−iii−i
χ1511111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111ii−i−i−ii−iii−i
χ1611111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111−i−iiii−ii−i−ii
χ17222222222222222-2-22222-2-22200000000-2-2000000000000-22-22-20000000000
χ18222222222222222-2-222-2-2-2-22200000000-2-20000000000002-22-220000000000
χ19222222222222222-2-2-2-222-2-2-2-20000000022000000000000-22-2-220000000000
χ20222222222222222-2-2-2-2-2-2-2-2-2-200000000220000000000002-222-20000000000
χ2122222222222-2-2-2-22-200222-2000000000000000022-2-222-2-22-2-2000000000000
χ2222222222222-2-2-2-22-200222-20000000000000000-2-222-2-2222-2-2000000000000
χ2322222222222-2-2-2-22-200-2-22-2000000000000000022-2-2-2-222-222000000000000
χ2422222222222-2-2-2-22-200-2-22-20000000000000000-2-22222-2-2-222000000000000
χ2522222222222-2-2-2-2-220022-22002222-2-2-2-20022-2-200000000-2-22000000000000
χ2622222222222-2-2-2-2-220022-2200-2-2-2-2222200-2-22200000000-2-22000000000000
χ2722222222222-2-2-2-2-2200-2-2-22002222-2-2-2-200-2-2220000000022-2000000000000
χ2822222222222-2-2-2-2-2200-2-2-2200-2-2-2-222220022-2-20000000022-2000000000000
χ294444444-4-4-4-40000400000-400000000000000000004i−4i0000000000000000000
χ304444444-4-4-4-40000400000-40000000000000000000−4i4i0000000000000000000
χ314444444-4-4-4-40000-4000004000000000000000004i−4i000000000000000000000
χ324444444-4-4-4-40000-400000400000000000000000−4i4i000000000000000000000
χ3344444-4-44-4-4444-4-40000000000000000004-4000000000000000000000000000
χ3444444-4-44-4-4444-4-4000000000000000000-44000000000000000000000000000
χ3544444-4-44-4-44-4-444004-400004-40000000000000000000000000000000000000
χ3644444-4-44-4-44-4-44400-440000-440000000000000000000000000000000000000
χ3744444-4-4-444-400000400000-4000000000000004-400000000000000000000000
χ3844444-4-4-444-400000400000-400000000000000-4400000000000000000000000
χ3944444-4-4-444-400000-40000040000000000004-40000000000000000000000000
χ4044444-4-4-444-400000-4000004000000000000-440000000000000000000000000
χ4144-44-400400-4004-4000400000-42i2i−2i−2i2i2i−2i−2i00000000002i−2i2i−2i000000000000000
χ4244-44-400400-4004-4000400000-4−2i−2i2i2i−2i−2i2i2i0000000000−2i2i−2i2i000000000000000
χ4344-44-400400-4004-4000-40000042i2i−2i−2i2i2i−2i−2i0000000000−2i2i−2i2i000000000000000
χ4444-44-400400-4004-4000-4000004−2i−2i2i2i−2i−2i2i2i00000000002i−2i2i−2i000000000000000
χ4544-44-400400-400-4400400000-402i2i−2i−2i−2i−2i2i2i00000000002i−2i−2i2i000000000000000
χ4644-44-400400-400-4400400000-40−2i−2i2i2i2i2i−2i−2i0000000000−2i2i2i−2i000000000000000
χ4744-44-400400-400-4400-400000402i2i−2i−2i−2i−2i2i2i0000000000−2i2i2i−2i000000000000000
χ4844-44-400400-400-4400-40000040−2i−2i2i2i2i2i−2i−2i00000000002i−2i−2i2i000000000000000
χ49888-8-88-800000000000000000000004i−4i4i−4i00000000000000000000000000000
χ50888-8-88-80000000000000000000000−4i4i−4i4i00000000000000000000000000000
χ51888-8-8-880000000000000000004i−4i4i−4i000000000000000000000000000000000
χ52888-8-8-88000000000000000000−4i4i−4i4i000000000000000000000000000000000
χ5388-88-800-80088-80000000000000000000000000000000000000000000000000
χ5488-88-800-8008-880000000000000000000000000000000000000000000000000
χ5588-8-880008-800000000000000000004-4-4400000000000000000000000000000
χ5688-8-880008-80000000000000000000-444-400000000000000000000000000000
χ5788-8-88000-880000000000000004-4-44000000000000000000000000000000000
χ5888-8-88000-88000000000000000-444-4000000000000000000000000000000000
χ5916-16000000000000000004-400000000000000000000000000000002i−2i2i−2i000000
χ6016-16000000000000000004-40000000000000000000000000000000−2i2i−2i2i000000
χ6116-1600000000000000000-4400000000000000000000000000000002-2-22000000
χ6216-1600000000000000000-440000000000000000000000000000000-222-2000000

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