Finite Group Databasebeta

← Group #72287086

Character table — Group #72287086

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size112222222444444888888888888816161616161616161616161616161616161616323232323232323232323232323232323232323232323232323232326464646464646464646464
order12222444422444422222244444442222224444444448888444444444444444444444488888844488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-1111-1-111111111-1-111-1-1-1-1-1-1-11-1-1-1-1-1
χ311111111111111111111111111111111-1-1111-1-111111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111-11111
χ5111111111111111111111111111111-1-1111-1-1111111-1-1-1-11-1-11111-1-1111-1-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-111-1-1
χ6111111111111111111111111111111-1-1111-1-111-1-1-1-111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-111
χ7111111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-111-1111-1-1
χ911111111111111111-1-1111111111-1-11111-1111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-1-111
χ1011111111111111111-1-1111111111-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-11111111-1-1-1111-1-1
χ1111111111111111111-1-1111111111-1-111-1-1-111-1-111111111-1-1-11111-1-1-1-1-111-1-1-1-111111111-1-1-111-1-1-1-111-1-1
χ1211111111111111111-1-1111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-111111-1-111-11-1-111
χ1311111111111111111-1-1111111111-1-1-1-111-1-1-1111111-1-1-1-1-111-1-1-1-111-111-1-1-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1
χ1411111111111111111-1-1111111111-1-1-1-111-1-1-111-1-1-1-11111-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-11-11111
χ1511111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1111111
χ1611111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1
χ17222222222222222-2-222-2-2-2-2-222-22-2-200002000022220000-2000000002000000000000-2-20022-20000000000
χ18222222222222222-2-222-2-2-2-2-222-22-2-2000020000-2-2-2-20000-20000000020000000000002200-2-220000000000
χ19222222222222222-2-2-2-2-2-2-2-2-222-22220000-2000022220000200000000-2000000000000-2-200-2-220000000000
χ20222222222222222-2-2-2-2-2-2-2-2-222-22220000-20000-2-2-2-20000200000000-2000000000000220022-20000000000
χ2122222222222-2-2222-2222-22-2-2-2-22-2-2-200002000000002222200000022-200-2-200000000000000000000-20000
χ2222222222222-2-2222-2222-22-2-2-2-22-2-2-20000200000000-2-2-2-22000000-2-2-200220000000000000000000020000
χ2322222222222-2-2222-2-2-22-22-2-2-2-22-2220000-2000000002222-2000000-2-2200-2-20000000000000000000020000
χ2422222222222-2-2222-2-2-22-22-2-2-2-22-2220000-200000000-2-2-2-2-2000000222002200000000000000000000-20000
χ2522222222222-2-222-2222-22-222-2-2-2-22222002220000000000-222000000-200000000000000-2-20000000-200000
χ2622222222222-2-222-2222-22-222-2-2-2-222-2-2002-2-20000000000-2-2-2000000-200000000000000220000000200000
χ2722222222222-2-222-22-2-2-22-222-2-2-2-2-2-22200-22200000000002-2-2000000200000000000000-2-20000000200000
χ2822222222222-2-222-22-2-2-22-222-2-2-2-2-2-2-2-200-2-2-20000000000222000000200000000000000220000000-200000
χ2922222-2-2-2-2-2-22222-2200-222-2-22-22-2002-20002-2000000000000022-2-20000000000022-2-2002-20000000000000
χ3022222-2-2-2-2-2-22222-2200-222-2-22-22-2002-20002-20000000000000-2-22200000000000-2-222002-20000000000000
χ3122222-2-2-2-2-2-22222-2200-222-2-22-22-200-22000-22000000000000022-2-200000000000-2-22200-220000000000000
χ3222222-2-2-2-2-2-22222-2200-222-2-22-22-200-22000-220000000000000-2-2220000000000022-2-200-220000000000000
χ3322222-2-2-2-2-2-2-2-222220022-2-2-2-22-22002-22202-2-2-20000000000000000002-20022-2-2000000-220000000000000
χ3422222-2-2-2-2-2-2-2-222220022-2-2-2-22-22002-2-2-202-222000000000000000000-2200-2-222000000-220000000000000
χ3522222-2-2-2-2-2-2-2-222220022-2-2-2-22-2200-22220-22-2-20000000000000000002-200-2-2220000002-20000000000000
χ3622222-2-2-2-2-2-2-2-222220022-2-2-2-22-2200-22-2-20-2222000000000000000000-220022-2-20000002-20000000000000
χ3722-2-2222-2-22-2222-2-22002-222-2-2-2-220000000000000002i2i−2i−2i0000000000002i−2i00002i−2i2i−2i00000000000002-200
χ3822-2-2222-2-22-2222-2-22002-222-2-2-2-220000000000000002i2i−2i−2i0000000000002i−2i0000−2i2i−2i2i0000000000000-2200
χ3922-2-2222-2-22-2222-2-22002-222-2-2-2-22000000000000000−2i−2i2i2i000000000000−2i2i00002i−2i2i−2i0000000000000-2200
χ4022-2-2222-2-22-2222-2-22002-222-2-2-2-22000000000000000−2i−2i2i2i000000000000−2i2i0000−2i2i−2i2i00000000000002-200
χ4122-2-2222-2-22-2-2-22-2-2-200222-2222-2-20000000000000002i2i−2i−2i000000000000−2i2i2-22-200000000000002i−2i000000
χ4222-2-2222-2-22-2-2-22-2-2-200222-2222-2-20000000000000002i2i−2i−2i000000000000−2i2i-22-220000000000000−2i2i000000
χ4322-2-2222-2-22-2-2-22-2-2-200222-2222-2-2000000000000000−2i−2i2i2i0000000000002i−2i2-22-20000000000000−2i2i000000
χ4422-2-2222-2-22-2-2-22-2-2-200222-2222-2-2000000000000000−2i−2i2i2i0000000000002i−2i-22-2200000000000002i−2i000000
χ4522-2-22-2-222-22222-22200-2-22-22-22-2-20000000000022-2-200000000000000000000002i−2i−2i2i2-2000002i−2i00000000
χ4622-2-22-2-222-22222-22200-2-22-22-22-2-20000000000022-2-20000000000000000000000−2i2i2i−2i2-200000−2i2i00000000
χ4722-2-22-2-222-22222-22200-2-22-22-22-2-200000000000-2-22200000000000000000000002i−2i−2i2i-2200000−2i2i00000000
χ4822-2-22-2-222-22222-22200-2-22-22-22-2-200000000000-2-2220000000000000000000000−2i2i2i−2i-22000002i−2i00000000
χ4922-2-22-2-222-22222-2-2-20022-22-2-222-20000000000022-2-20000000000000000002-2-220000-2200000000000002-2
χ5022-2-22-2-222-22222-2-2-20022-22-2-222-20000000000022-2-2000000000000000000-222-20000-220000000000000-22
χ5122-2-22-2-222-22222-2-2-20022-22-2-222-200000000000-2-2220000000000000000002-2-2200002-20000000000000-22
χ5222-2-22-2-222-22222-2-2-20022-22-2-222-200000000000-2-222000000000000000000-222-200002-200000000000002-2
χ53444444444-4-400-4-40044000000000000022-40022000000000002-22-2000-2-2000000000000000000000000000
χ54444444444-4-400-4-400440000000000000-2-2-400-2-200000000000-22-2200022000000000000000000000000000
χ55444444444-4-400-4-400-4-40000000000000224002200000000000-22-22000-2-2000000000000000000000000000
χ56444444444-4-400-4-400-4-40000000000000-2-2400-2-2000000000002-22-200022000000000000000000000000000
χ5744444-4-4-4-44400-4-400000000000004-40022000-2-2000000000002-2-22000-22000000000000000000000000000
χ5844444-4-4-4-44400-4-400000000000004-400-2-20002200000000000-222-20002-2000000000000000000000000000
χ5944444-4-4-4-44400-4-40000000000000-440022000-2-200000000000-222-2000-22000000000000000000000000000
χ6044444-4-4-4-44400-4-40000000000000-4400-2-200022000000000002-2-220002-2000000000000000000000000000
χ6144444-4-4-4-4-4-444444-4004-4-4444-4-4-40000000000000000000000000000000000000000000000000000000000
χ6244444-4-4-4-4-4-4-4-444-4-400-4-4444-44440000000000000000000000000000000000000000000000000000000000
χ63444-4-44-44-4000000004-40000000000022000-2-2002i−2i2i−2i2i−2i2i−2i02-200002i−2i000000000000000002i−2i00000000000
χ64444-4-44-44-4000000004-40000000000022000-2-200−2i2i−2i2i−2i2i−2i2i02-20000−2i2i00000000000000000−2i2i00000000000
χ65444-4-44-44-4000000004-400000000000-2-200022002i−2i2i−2i−2i2i−2i2i0-220000−2i2i000000000000000002i−2i00000000000
χ66444-4-44-44-4000000004-400000000000-2-20002200−2i2i−2i2i2i−2i2i−2i0-2200002i−2i00000000000000000−2i2i00000000000
χ67444-4-44-44-400000000-440000000000022000-2-2002i−2i2i−2i2i−2i2i−2i0-220000−2i2i00000000000000000−2i2i00000000000
χ68444-4-44-44-400000000-440000000000022000-2-200−2i2i−2i2i−2i2i−2i2i0-2200002i−2i000000000000000002i−2i00000000000
χ69444-4-44-44-400000000-4400000000000-2-200022002i−2i2i−2i−2i2i−2i2i02-200002i−2i00000000000000000−2i2i00000000000
χ70444-4-44-44-400000000-4400000000000-2-20002200−2i2i−2i2i2i−2i2i−2i02-20000−2i2i000000000000000002i−2i00000000000
χ7144-4-4444-4-44-4444-44-400-44-4-44-4-4440000000000000000000000000000000000000000000000000000000000
χ7244-4-4444-4-44-4-4-44-44400-4-4-44-4444-40000000000000000000000000000000000000000000000000000000000
χ7344-4-44-4-444-44-4-44-44-400-4444-44-4-440000000000000000000000000000000000000000000000000000000000
χ7444-4-44-4-444-44-4-44-4-44004-4-4-444-4440000000000000000000000000000000000000000000000000000000000
χ75888-8-8-88-880000000000000000000004-4000-440000000000000000000000000000000000000000000000000
χ76888-8-8-88-88000000000000000000000-440004-40000000000000000000000000000000000000000000000000
χ7788-88-88-8-8800000000000000000000000000000000004-4-44000000000000000000000000000000000000000
χ7888-88-88-8-880000000000000000000000000000000000-444-4000000000000000000000000000000000000000
χ7988-88-8-888-80000000000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ8088-88-8-888-8000000000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ8188-8-8888-8-8-8800-8800000000000000000000000000000000000000000000000000000000000000000000000
χ8288-8-88-8-8888-800-8800000000000000000000000000000000000000000000000000000000000000000000000
χ8316-160000000008i−8i00000000000000000004-40004i−4i00000000000000000000000000000000000000000000000
χ8416-160000000008i−8i0000000000000000000-44000−4i4i00000000000000000000000000000000000000000000000
χ8516-16000000000−8i8i00000000000000000004-4000−4i4i00000000000000000000000000000000000000000000000
χ8616-16000000000−8i8i0000000000000000000-440004i−4i00000000000000000000000000000000000000000000000

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