Finite Group Databasebeta

← Group #72325871

Character table — Group #72325871

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11222444444161616161616161632323232323232323232323232323232323232323232323232323264646464128128128128128128
order12222222222222224442224444444444444444444444444444888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ411111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111
χ51111111111111111111-11-1-11-1-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-111-1-1
χ61111111111111111111-11-1-11-1-1-111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-111-1-111
χ71111111111111111111-1-11-1-11-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-111
χ81111111111111111111-1-11-1-11-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1
χ911111111111111-1-111111-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1ii−i−ii−ii−ii−i
χ1011111111111111-1-111111-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1−i−iii−ii−ii−ii
χ1111111111111111-1-11111-111-1111-1-111-1-1-1-11111-1-1-1-1-1-1-1ii−i−ii−i−ii−ii
χ1211111111111111-1-11111-111-1111-1-111-1-1-1-11111-1-1-1-1-1-1-1−i−iii−iii−ii−i
χ1311111111111111-1-1111-111-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1ii−i−i−iii−i−ii
χ1411111111111111-1-1111-111-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1−i−iiii−i−iii−i
χ1511111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1ii−i−i−ii−iii−i
χ1611111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1−i−iiii−ii−i−ii
χ17222222222222-2-2222-2-20020020000-2-20000000022-2-22-2-20000000000
χ18222222222222-2-2222-2-200-200-200002200000000-2-2222-2-20000000000
χ19222222222222-2-2-2-22-2-20020020000-2-200000000-2-222-2220000000000
χ20222222222222-2-2-2-22-2-200-200-20000220000000022-2-2-2220000000000
χ2122222222222-22-222-22-202002000-2-200000022-2-20000-22-20000000000
χ2222222222222-22-222-22-20-200-200022000000-2-2220000-22-20000000000
χ2322222222222-22-2-2-2-22-202002000-2-2000000-2-22200002-220000000000
χ2422222222222-22-2-2-2-22-20-200-20002200000022-2-200002-220000000000
χ2522222222222-2-2222-2-22200200-2-2000022-2-200000000-2-220000000000
χ2622222222222-2-2222-2-22-200-200220000-2-22200000000-2-220000000000
χ2722222222222-2-22-2-2-2-22200200-2-20000-2-2220000000022-20000000000
χ2822222222222-2-22-2-2-2-22-200-20022000022-2-20000000022-20000000000
χ294444444-4-4-4-40040000-4000000000000004-4000000000000000000000
χ304444444-4-4-4-40040000-400000000000000-44000000000000000000000
χ314444444-4-4-4-400-4000040000000000004-400000000000000000000000
χ324444444-4-4-4-400-400004000000000000-4400000000000000000000000
χ3344444-4-444-4-4040000-4000000000000000004-40000000000000000000
χ3444444-4-444-4-4040000-400000000000000000-440000000000000000000
χ3544444-4-444-4-40-40000400000000000000000004-400000000000000000
χ3644444-4-444-4-40-4000040000000000000000000-4400000000000000000
χ3744444-4-4-4-44440000-400000000000000000000004-4000000000000000
χ3844444-4-4-4-44440000-40000000000000000000000-44000000000000000
χ3944444-4-4-4-444-4000040000000000000000000000004-40000000000000
χ4044444-4-4-4-444-400004000000000000000000000000-440000000000000
χ41888-8-800008-80000000000000000004-40000000000000000000000000
χ42888-8-800008-8000000000000000000-440000000000000000000000000
χ43888-8-80000-880000000000400-40000000000000000000000000000000
χ44888-8-80000-880000000000-40040000000000000000000000000000000
χ4588-88-8008-80000000000000000004-4000000000000000000000000000
χ4688-88-8008-8000000000000000000-44000000000000000000000000000
χ4788-88-800-8800000000000400-400000000000000000000000000000000
χ4888-88-800-8800000000000-400400000000000000000000000000000000
χ4988-8-888-80000000000000000004-400000000000000000000000000000
χ5088-8-888-8000000000000000000-4400000000000000000000000000000
χ5188-8-88-88000000000000400-4000000000000000000000000000000000
χ5288-8-88-88000000000000-4004000000000000000000000000000000000
χ5316-160000000000004-40000000000000000000000000000002i−2i2i−2i000000
χ5416-160000000000004-4000000000000000000000000000000−2i2i−2i2i000000
χ5516-16000000000000-440000000000000000000000000000002-2-22000000
χ5616-16000000000000-44000000000000000000000000000000-222-2000000

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