Finite Group Databasebeta

← Group #311213

Character table — Group #311213

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-1111-11-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-1-1-11-11-1-1-1-1-1-111-1-1
χ411111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-111-1-1-1-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-111111-1
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-11-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11111-1-111-11
χ911111111111111111-1-1-1-11111111-1-111111111-1-1-1-111111-1-1-11-1-1-11111-1-1-1-1
χ1011111111111111111-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-11111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-11111-111-1-1-111-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-11111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-11-1111-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-111-11-1-1-1-1-11111-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-111111-1-111-1-1-1-11-1
χ17222222222-22-2-222-2-22222-2000000-2-2000022-2-20000000000020-20000000000
χ18222222222-22-2-222-2-22222-2000000-2-20000-2-22200000000000-2020000000000
χ19222222222-22-2-222-2-2-2-2-2-2-200000022000022-2-200000000000-2020000000000
χ20222222222-22-2-222-2-2-2-2-2-2-2000000220000-2-2220000000000020-20000000000
χ2122222222-22-222-2-22-20000-22222220022-2-2000000000000-2000-200000000000
χ2222222222-22-222-2-22-20000-22222-2-200-2-2-2-20000000000002000200000000000
χ2322222222-22-222-2-22-20000-2-2-2-2-22200-2-222000000000000-2000200000000000
χ2422222222-22-222-2-22-20000-2-2-2-2-2-2-20022220000000000002000-200000000000
χ25222-2-2-2-2222-2-2-22-22-2000022i2i−2i−2i0000002i−2i00000000000002i−2i0002-200000000
χ26222-2-2-2-2222-2-2-22-22-2000022i2i−2i−2i0000002i−2i0000000000000−2i2i000-2200000000
χ27222-2-2-2-2222-2-2-22-22-200002−2i−2i2i2i000000−2i2i00000000000002i−2i000-2200000000
χ28222-2-2-2-2222-2-2-22-22-200002−2i−2i2i2i000000−2i2i0000000000000−2i2i0002-200000000
χ29222-2-2-2-22-222-2-2-22222i2i−2i−2i-22i2i−2i−2i002i−2i00−2i2i000022-2-200000000000000000000
χ30222-2-2-2-22-222-2-2-22222i2i−2i−2i-2−2i−2i2i2i002i−2i002i−2i0000-2-22200000000000000000000
χ31222-2-2-2-22-222-2-2-2222−2i−2i2i2i-22i2i−2i−2i00−2i2i00−2i2i0000-2-22200000000000000000000
χ32222-2-2-2-22-222-2-2-2222−2i−2i2i2i-2−2i−2i2i2i00−2i2i002i−2i000022-2-200000000000000000000
χ33222-2-2-2-22-2-2222-22-2-22i2i−2i−2i2000000−2i2i00000000000022-2-20000000000002i−2i00
χ34222-2-2-2-22-2-2222-22-2-22i2i−2i−2i2000000−2i2i000000000000-2-222000000000000−2i2i00
χ35222-2-2-2-22-2-2222-22-2-2−2i−2i2i2i20000002i−2i00000000000022-2-2000000000000−2i2i00
χ36222-2-2-2-22-2-2222-22-2-2−2i−2i2i2i20000002i−2i000000000000-2-2220000000000002i−2i00
χ372-2-22-22-220202-200-20000002-22-22i−2i002i−2i002−22−200002−22−200000000i2−i2i2−i20000
χ382-2-22-22-220202-200-20000002-22-22i−2i002i−2i00−22−220000−22−2200000000−i2i2−i2i20000
χ392-2-22-22-220202-200-20000002-22-2−2i2i00−2i2i002−22−200002−22−200000000−i2i2−i2i20000
χ402-2-22-22-220202-200-20000002-22-2−2i2i00−2i2i00−22−220000−22−2200000000i2−i2i2−i20000
χ412-2-22-22-220202-200-2000000-22-222i−2i00−2i2i002−22−20000−22−2200000000i2−i2−i2i20000
χ422-2-22-22-220202-200-2000000-22-222i−2i00−2i2i00−22−2200002−22−200000000−i2i2i2−i20000
χ432-2-22-22-220202-200-2000000-22-22−2i2i002i−2i002−22−20000−22−2200000000−i2i2i2−i20000
χ442-2-22-22-220202-200-2000000-22-22−2i2i002i−2i00−22−2200002−22−200000000i2−i2−i2i20000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ46444-4-4-4-444-4-4444-4-440000-40000000000000000000000000000000000000000
χ474-4444-4-4-440400-4-4004-44-400000000000000000000000000000000000000000
χ484-4444-4-4-440400-4-400-44-4400000000000000000000000000000000000000000
χ494-4444-4-4-4-40-40044000000000000000000000002i2−2i22i2−2i200000000000000000000
χ504-4444-4-4-4-40-4004400000000000000000000000−2i22i2−2i22i200000000000000000000
χ514-44-4-444-440-400-44000000000000000000000002i2−2i2−2i22i200000000000000000000
χ524-44-4-444-440-400-4400000000000000000000000−2i22i22i2−2i200000000000000000000
χ534-44-4-444-4-404004-4004i−4i−4i4i00000000000000000000000000000000000000000
χ544-44-4-444-4-404004-400−4i4i4i−4i00000000000000000000000000000000000000000
χ554-4-44-44-440-40-4400400000000000000000022−22−2222000000000000000000000000
χ564-4-44-44-440-40-44004000000000000000000−222222−22000000000000000000000000
χ574-4-4-44-444040-4400-40000004i−4i−4i4i000000000000000000000000000000000000
χ584-4-4-44-444040-4400-4000000−4i4i4i−4i000000000000000000000000000000000000
χ594-4-4-44-4440-404-40040000000000000000000000000022−22−22220000000000000000
χ604-4-4-44-4440-404-400400000000000000000000000000−222222−220000000000000000
χ6188-88-8-88-8000000000000000000000000000000000000000000000000000000
χ6288-8-888-8-8000000000000000000000000000000000000000000000000000000

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