Finite Group Databasebeta

← Group #148285

Character table — Group #148285

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122222222222222222244444488888888888888888888888816161616161616161616161616161616
order124422222224444444888888888822448888161616161616161616161616161616164444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-111-1-11-1-1111111-1-1-1-11-11-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111-1-1-1-111-1-11-1-1111111-1-1-1-11-11-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111-1-1-1-111-1-11-1-1111111-1-1-1-11-11-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111-1-1-1-111-1-11-1-1111111-1-1-1-11-11-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111-1-1-1-111-1-11-1-1111111-1-1-1-1-11-11-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ141111111-1-1-1-111-1-11-1-1111111-1-1-1-1-11-11-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ151111111-1-1-1-111-1-11-1-1111111-1-1-1-1-11-11-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111-1-1-1-111-1-11-1-1111111-1-1-1-1-11-11-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ192222222-2-2-2-222-2-22-2-2-2-2-2-2-2-222222-22-2-2-22200000000000000000000000000000000
χ202222222-2-2-2-222-2-22-2-2-2-2-2-2-2-22222-22-2222-2-200000000000000000000000000000000
χ2122222-2-22-22-2-2-22-222-22222-2-222-2-2000000000000000022-2-222-2-20000000000000000
χ2222222-2-22-22-2-2-22-222-22222-2-222-2-20000000000000000-2-222-2-2220000000000000000
χ2322222-2-22-22-2-2-22-222-2-2-2-2-222-2-222000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ2422222-2-22-22-2-2-22-222-2-2-2-2-222-2-22200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ2522222-2-2-22-22-2-2-222-222222-2-2-2-222000000000000000022-2-2-2-2220000000000000000
χ2622222-2-2-22-22-2-2-222-222222-2-2-2-2220000000000000000-2-22222-2-20000000000000000
χ2722222-2-2-22-22-2-2-222-22-2-2-2-22222-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2822222-2-2-22-22-2-2-222-22-2-2-2-22222-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2922-2-22222222-2-2-2-2-2-2-200000000002-2-220000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3022-2-22222222-2-2-2-2-2-2-200000000002-2-220000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3122-2-22222222-2-2-2-2-2-2-20000000000-222-20000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ3222-2-22222222-2-2-2-2-2-2-20000000000-222-20000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ3322-2-2222-2-2-2-2-2-222-222000000000022-2-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ3422-2-2222-2-2-2-2-2-222-222000000000022-2-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ3522-2-2222-2-2-2-2-2-222-2220000000000-2-2220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ3622-2-2222-2-2-2-2-2-222-2220000000000-2-2220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ3722-2-22-2-22-22-222-22-2-22000000000000002i−2i2i−2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ3822-2-22-2-22-22-222-22-2-22000000000000002i−2i2i−2i−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ3922-2-22-2-22-22-222-22-2-2200000000000000−2i2i−2i2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ4022-2-22-2-22-22-222-22-2-2200000000000000−2i2i−2i2i−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ4122-2-22-2-2-22-22222-2-22-2000000000000002i−2i−2i2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ4222-2-22-2-2-22-22222-2-22-2000000000000002i−2i−2i2i−222−22−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ4322-2-22-2-2-22-22222-2-22-200000000000000−2i2i2i−2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ4422-2-22-2-2-22-22222-2-22-200000000000000−2i2i2i−2i−222−22−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ4522-2-2-22-222-2-22-22-22-2222-2-22-22-22-200000000000000000000000000002i−2i2i−2i00000000
χ4622-2-2-22-222-2-22-22-22-2222-2-22-22-22-20000000000000000000000000000−2i2i−2i2i00000000
χ4722-2-2-22-222-2-22-22-22-22-2-222-22-22-220000000000000000000000002i−2i2i−2i000000000000
χ4822-2-2-22-222-2-22-22-22-22-2-222-22-22-22000000000000000000000000−2i2i−2i2i000000000000
χ4922-2-2-22-2-2-2222-2-2222-222-2-22-2-22-2200000000000000000000000000002-2-2200000000
χ5022-2-2-22-2-2-2222-2-2222-222-2-22-2-22-220000000000000000000000000000-222-200000000
χ5122-2-2-22-2-2-2222-2-2222-2-2-222-222-22-20000000000000000000000002-2-22000000000000
χ5222-2-2-22-2-2-2222-2-2222-2-2-222-222-22-2000000000000000000000000-222-2000000000000
χ5322-2-2-2-222-2-22-22222-2-222-2-2-222-2-22000000000000000000000000000000002i−2i2i−2i0000
χ5422-2-2-2-222-2-22-22222-2-222-2-2-222-2-2200000000000000000000000000000000−2i2i−2i2i0000
χ5522-2-2-2-222-2-22-22222-2-2-2-2222-2-222-20000000000000000000000000000000000002i−2i2i−2i
χ5622-2-2-2-222-2-22-22222-2-2-2-2222-2-222-2000000000000000000000000000000000000−2i2i−2i2i
χ5722-2-2-2-22-222-2-22-2-222222-2-2-22-222-2000000000000000000000000000000002-2-220000
χ5822-2-2-2-22-222-2-22-2-222222-2-2-22-222-200000000000000000000000000000000-222-20000
χ5922-2-2-2-22-222-2-22-2-2222-2-2222-22-2-220000000000000000000000000000000000002-2-22
χ6022-2-2-2-22-222-2-22-2-2222-2-2222-22-2-22000000000000000000000000000000000000-222-2
χ614444-44-444-4-4-44-44-44-400000000000000000000000000000000000000000000000000
χ624444-44-4-4-444-444-4-4-4400000000000000000000000000000000000000000000000000
χ634444-4-444-4-444-4-4-4-44400000000000000000000000000000000000000000000000000
χ644444-4-44-444-44-444-4-4-400000000000000000000000000000000000000000000000000
χ658-88i−8i0000000000000042−424i2−4i20000000000000000000000000000000000000000000000
χ668-88i−8i00000000000000−4242−4i24i20000000000000000000000000000000000000000000000
χ678-8−8i8i0000000000000042−42−4i24i20000000000000000000000000000000000000000000000
χ688-8−8i8i00000000000000−42424i2−4i20000000000000000000000000000000000000000000000

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