Finite Group Databasebeta

← Group #12021

Character table — Group #12021

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222222222222222244444444444444444444441616161616161616
order12224444444444888888882488881616161616161616161616161616161688888888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ61111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii
χ71111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii
χ81111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i
χ91111-1-1-1-1111111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-1
χ101111-1-1-1-1111111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11
χ111111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111111-11-1-11-11
χ121111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-11-111-11-1
χ131111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111i−i−iii−i−ii
χ141111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111−iii−i−iii−i
χ151111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1i−i−ii−iii−i
χ161111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1−iii−ii−i−ii
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ182222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222-2-2-2-222-2-2000000002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ20222222-2-2-2-222-2-2000000002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ21222222-2-2-2-2-2-22200000000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ22222222-2-2-2-2-2-22200000000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ232222-2-222-2-222-2-200000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ242222-2-222-2-222-2-200000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ252222-2-222-2-2-2-222000000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ262222-2-222-2-2-2-222000000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ272222-2-2-2-22222222222-2-2-2-2-2-2-2-222000000000000000000000000
χ282222-2-2-2-222-2-2-2-22222-2-2-2-22222-2-2000000000000000000000000
χ2922-2-200002-22i−2i2i−2i000022-2-2002i−2i0000002i−2i2i−2i00002-22-200000000
χ3022-2-200002-22i−2i2i−2i000022-2-2002i−2i000000−2i2i−2i2i0000-22-2200000000
χ3122-2-200002-22i−2i2i−2i0000-2-22200−2i2i002i−2i2i−2i00002-22-2000000000000
χ3222-2-200002-22i−2i2i−2i0000-2-22200−2i2i00−2i2i−2i2i0000-22-22000000000000
χ3322-2-200002-2−2i2i−2i2i000022-2-200−2i2i0000002i−2i2i−2i0000-22-2200000000
χ3422-2-200002-2−2i2i−2i2i000022-2-200−2i2i000000−2i2i−2i2i00002-22-200000000
χ3522-2-200002-2−2i2i−2i2i0000-2-222002i−2i002i−2i2i−2i0000-22-22000000000000
χ3622-2-200002-2−2i2i−2i2i0000-2-222002i−2i00−2i2i−2i2i00002-22-2000000000000
χ3722-2-20000-222i−2i−2i2i22-2-2000000002i−2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i200000000
χ3822-2-20000-222i−2i−2i2i22-2-2000000002i−2i−222−2−222−2i2−i2−i2i2i2−i2−i2i200000000
χ3922-2-20000-222i−2i−2i2i-2-22200000000−2i2i2−2−22−222−2−i2i2i2−i2i2−i2−i2i200000000
χ4022-2-20000-222i−2i−2i2i-2-22200000000−2i2i−222−22−2−22i2−i2−i2i2−i2i2i2−i200000000
χ4122-2-20000-22−2i2i2i−2i22-2-200000000−2i2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i200000000
χ4222-2-20000-22−2i2i2i−2i22-2-200000000−2i2i−222−2−222−2−i2i2i2−i2−i2i2i2−i200000000
χ4322-2-20000-22−2i2i2i−2i-2-222000000002i−2i2−2−22−222−2i2−i2−i2i2−i2i2i2−i200000000
χ4422-2-20000-22−2i2i2i−2i-2-222000000002i−2i−222−22−2−22−i2i2i2−i2i2−i2−i2i200000000
χ454-44-4004i−4i00000022−2222−222i2−2i22i2−2i2000000000000000000000000000000
χ464-44-4004i−4i000000−2222−2222−2i22i2−2i22i2000000000000000000000000000000
χ474-44-400−4i4i00000022−2222−22−2i22i2−2i22i2000000000000000000000000000000
χ484-44-400−4i4i000000−2222−22222i2−2i22i2−2i2000000000000000000000000000000
χ494-4-444i−4i0000000022−22−22222i2−2i2−2i22i2000000000000000000000000000000
χ504-4-444i−4i00000000−222222−22−2i22i22i2−2i2000000000000000000000000000000
χ514-4-44−4i4i0000000022−22−2222−2i22i22i2−2i2000000000000000000000000000000
χ524-4-44−4i4i00000000−222222−222i2−2i2−2i22i2000000000000000000000000000000

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