Finite Group Databasebeta

← Group #281144

Character table — Group #281144

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-11-1
χ911111111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11-1-1-11111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1111-1-1-1-1111-1
χ17222222222-222-2-2-22-22222-20000000022-2-20000-2-222-2-2000000000000000000000000
χ18222222222-222-2-2-22-22222-200000000-2-2-2-2000022-2-222000000000000000000000000
χ19222222222-222-2-2-22-2-2-2-2-2-20000000022220000-2-2-2-222000000000000000000000000
χ20222222222-222-2-2-22-2-2-2-2-2-200000000-2-22200002222-2-2000000000000000000000000
χ2122222222-22-2-2222-2-20000-22222-2-2-2-200002222000000000000000000-2-20000000000
χ2222222222-22-2-2222-2-20000-22222-2-2-2-20000-2-2-2-2000000000000000000220000000000
χ2322222222-22-2-2222-2-20000-2-2-2-2-22222000022-2-2000000000000000000-220000000000
χ2422222222-22-2-2222-2-20000-2-2-2-2-222220000-2-2220000000000000000002-20000000000
χ25222-2-2-2-22-202-2000202i2i−2i−2i022−2−222−2−22-2000000002i−2i00i2i2−i2−i222−2−2i2i2−i2−i2000000000000
χ26222-2-2-2-22-202-2000202i2i−2i−2i022−2−222−2−2-2200000000−2i2i00i2i2−i2−i2−2−222−i2−i2i2i2000000000000
χ27222-2-2-2-22-202-2000202i2i−2i−2i0−2−222−2−2222-2000000002i−2i00−i2−i2i2i2−2−222−i2−i2i2i2000000000000
χ28222-2-2-2-22-202-2000202i2i−2i−2i0−2−222−2−222-2200000000−2i2i00−i2−i2i2i222−2−2i2i2−i2−i2000000000000
χ29222-2-2-2-22-202-200020−2i−2i2i2i022−2−222−2−22-200000000−2i2i00−i2−i2i2i222−2−2−i2−i2i2i2000000000000
χ30222-2-2-2-22-202-200020−2i−2i2i2i022−2−222−2−2-22000000002i−2i00−i2−i2i2i2−2−222i2i2−i2−i2000000000000
χ31222-2-2-2-22-202-200020−2i−2i2i2i0−2−222−2−2222-200000000−2i2i00i2i2−i2−i2−2−222i2i2−i2−i2000000000000
χ32222-2-2-2-22-202-200020−2i−2i2i2i0−2−222−2−222-22000000002i−2i00i2i2−i2−i222−2−2−i2−i2i2i2000000000000
χ3322-22-22-2-2-20-22000202-22-202−22−22−22−2000000002i−2i002i−2i2−22−2i2−i2i2−i2i2−i2i2−i2000000000000
χ3422-22-22-2-2-20-22000202-22-202−22−22−22−200000000−2i2i00−2i2i2−22−2−i2i2−i2i2−i2i2−i2i2000000000000
χ3522-22-22-2-2-20-22000202-22-20−22−22−22−22000000002i−2i002i−2i−22−22−i2i2−i2i2−i2i2−i2i2000000000000
χ3622-22-22-2-2-20-22000202-22-20−22−22−22−2200000000−2i2i00−2i2i−22−22i2−i2i2−i2i2−i2i2−i2000000000000
χ3722-22-22-2-2-20-2200020-22-2202−22−22−22−2000000002i−2i00−2i2i−22−22i2−i2i2−i2−i2i2−i2i2000000000000
χ3822-22-22-2-2-20-2200020-22-2202−22−22−22−200000000−2i2i002i−2i−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ3922-22-22-2-2-20-2200020-22-220−22−22−22−22000000002i−2i00−2i2i2−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ4022-22-22-2-2-20-2200020-22-220−22−22−22−2200000000−2i2i002i−2i2−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ4122-2-22-22-222-2-2-22-22-22i−2i−2i2i200000000002i−2i000000000000002i−2i−2i2i-222-2000000000000
χ4222-2-22-22-222-2-2-22-22-22i−2i−2i2i200000000002i−2i00000000000000−2i2i2i−2i2-2-22000000000000
χ4322-2-22-22-222-2-2-22-22-2−2i2i2i−2i20000000000−2i2i000000000000002i−2i−2i2i2-2-22000000000000
χ4422-2-22-22-222-2-2-22-22-2−2i2i2i−2i20000000000−2i2i00000000000000−2i2i2i−2i-222-2000000000000
χ4522-2-22-22-22-2-2-22-22222i−2i−2i2i-22-2-222-2-2200−2i2i00000000002i−2i−2i2i00000000000000000000
χ4622-2-22-22-22-2-2-22-22222i−2i−2i2i-2-222-2-222-200−2i2i0000000000−2i2i2i−2i00000000000000000000
χ4722-2-22-22-22-2-2-22-2222−2i2i2i−2i-22-2-222-2-22002i−2i0000000000−2i2i2i−2i00000000000000000000
χ4822-2-22-22-22-2-2-22-2222−2i2i2i−2i-2-222-2-222-2002i−2i00000000002i−2i−2i2i00000000000000000000
χ4922-2-22-22-2-2-2222-22-2-2000022-2-22-222-200000000000000000000000000002i−2i2i−2i000000
χ5022-2-22-22-2-2-2222-22-2-2000022-2-22-222-20000000000000000000000000000−2i2i−2i2i000000
χ5122-2-22-22-2-2-2222-22-2-200002-222-22-2-2200000000000000000000000000002i−2i−2i2i000000
χ5222-2-22-22-2-2-2222-22-2-200002-222-22-2-220000000000000000000000000000−2i2i2i−2i000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-4-4-4440-44000-40000002222−22−22−22−22222200000000000000000000000000000000000000
χ55444-4-4-4-4440-44000-4000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-44-44-4-4404-4000-400000022−2222−22−2222−222200000000000000000000000000000000000000
χ5744-44-44-4-4404-4000-4000000−2222−222222−2222−2200000000000000000000000000000000000000
χ5844-4-44-44-4-4444-44-4-440000-40000000000000000000000000000000000000000000000
χ594-44-4-444-40400-4-44000000000000000000000000000000000000000000000002i2−2i20000
χ604-44-4-444-40400-4-4400000000000000000000000000000000000000000000000−2i22i20000
χ614-44-4-444-40-40044-400000000000000000004i−4i00000000000000000000000000000000
χ624-44-4-444-40-40044-40000000000000000000−4i4i00000000000000000000000000000000
χ634-4-44-4-44404004-4-40000000000000000000004i−4i000000000000000000000000000000
χ644-4-44-4-44404004-4-4000000000000000000000−4i4i000000000000000000000000000000
χ654-4-44-4-4440-400-444000000000000000000000000000000000000000000000000022−2200
χ664-4-44-4-4440-400-4440000000000000000000000000000000000000000000000000−222200
χ678-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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