Finite Group Databasebeta

← Group #292516

Character table — Group #292516

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444444444444448888888888888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-1-111111-1-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-111-11111-1-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-1-1-111
χ91111111111111111-1-1-1-1-1-111111-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-11-1
χ101111111111111111-1-1-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-1-111-11
χ111111111111111111-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111-1-1-111-11
χ121111111111111111-1-1-1-1-1-111111-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-111111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1111-1
χ172222222222-2-2-222-22222-2-22222-2-2-2-2-2-200-2-222000000000000000000000000000000
χ182222222222-2-2-222-22222-2-2-2-2-2-2-2-2-2-2220022-2-2000000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2222222-222-2-2-20022-2-2000000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-222-2-2-2-2-222-22200-2-222000000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2220000-2-2-2-200220000-2-2000000000000000000200-2000000
χ2222222222-2-2222-2-2222-2-2220000-2-2-2-200-2-2000022000000000000000000-2002000000
χ2322222222-2-2222-2-22-2-222-2-20000-222-20022000022000000000000000000-200-2000000
χ2422222222-2-2222-2-22-2-222-2-20000-222-200-2-20000-2-20000000000000000002002000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-200002222000000000000000000000000002-202-20000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-20000222200000000000000000000000000-220-220000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200002-2-22000000000000000000000000002-20-220000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200002-2-2200000000000000000000000000-2202-20000000
χ29222-2-22-2-2-2-20002202-22-2002i2i−2i−2i00000000002i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ30222-2-22-2-2-2-20002202-22-2002i2i−2i−2i00000000002i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ31222-2-22-2-2-2-20002202-22-200−2i−2i2i2i0000000000−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ32222-2-22-2-2-2-20002202-22-200−2i−2i2i2i0000000000−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ33222-2-22-2-2-2-2000220-22-22002i2i−2i−2i0000000000−2i2i0022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ34222-2-22-2-2-2-2000220-22-22002i2i−2i−2i0000000000−2i2i00−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ35222-2-22-2-2-2-2000220-22-2200−2i−2i2i2i00000000002i−2i0022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ36222-2-22-2-2-2-2000220-22-2200−2i−2i2i2i00000000002i−2i00−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ3722-22-2-22-22-20002-2000002i−2i2-22-202i−2i000002i−2i0000i2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ3822-22-2-22-22-20002-2000002i−2i2-22-202i−2i000002i−2i0000−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ3922-22-2-22-22-20002-2000002i−2i-22-2202i−2i00000−2i2i0000i2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ4022-22-2-22-22-20002-2000002i−2i-22-2202i−2i00000−2i2i0000−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ4122-22-2-22-22-20002-200000−2i2i2-22-20−2i2i00000−2i2i0000i2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ4222-22-2-22-22-20002-200000−2i2i2-22-20−2i2i00000−2i2i0000−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ4322-22-2-22-22-20002-200000−2i2i-22-220−2i2i000002i−2i0000i2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ4422-22-2-22-22-20002-200000−2i2i-22-220−2i2i000002i−2i0000−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ4522-2-22-2-22-2222-22-2-20000002i−2i−2i2i-20022i−2i000000002i−2i−2i2i0000-222-20000000000000000
χ4622-2-22-2-22-2222-22-2-20000002i−2i−2i2i-20022i−2i00000000−2i2i2i−2i00002-2-220000000000000000
χ4722-2-22-2-22-2222-22-2-2000000−2i2i2i−2i-2002−2i2i000000002i−2i−2i2i00002-2-220000000000000000
χ4822-2-22-2-22-2222-22-2-2000000−2i2i2i−2i-2002−2i2i00000000−2i2i2i−2i0000-222-20000000000000000
χ4922-2-22-2-22-22-2-222-220000002i−2i−2i2i200-2−2i2i0000000000002-2-2200002i−2i−2i2i000000000000
χ5022-2-22-2-22-22-2-222-220000002i−2i−2i2i200-2−2i2i000000000000-222-20000−2i2i2i−2i000000000000
χ5122-2-22-2-22-22-2-222-22000000−2i2i2i−2i200-22i−2i0000000000002-2-220000−2i2i2i−2i000000000000
χ5222-2-22-2-22-22-2-222-22000000−2i2i2i−2i200-22i−2i000000000000-222-200002i−2i−2i2i000000000000
χ53444-4-44-4-444000-4-404-4-44000000000000000000000000000000000000000000000000
χ54444-4-44-4-444000-4-40-444-4000000000000000000000000000000000000000000000000
χ5544-44-4-44-4-44000-44000004i−4i00000−4i4i000000000000000000000000000000000000000
χ5644-44-4-44-4-44000-4400000−4i4i000004i−4i000000000000000000000000000000000000000
χ5744-4-44-4-444-444-4-44-40000000000400-400000000000000000000000000000000000000
χ5844-4-44-4-444-4-4-44-4440000000000-400400000000000000000000000000000000000000
χ594-4444-4-4-4004-4400-400000000000000004-40000000000000000000000000000000000
χ604-4444-4-4-4004-4400-40000000000000000-440000000000000000000000000000000000
χ614-4444-4-4-400-44-400400000000000000000000004i−4i0000000000000000000000000000
χ624-4444-4-4-400-44-40040000000000000000000000−4i4i0000000000000000000000000000
χ634-4-4-4444-4004-4-4004000000000000000000000000000000000000000000000022−220000
χ644-4-4-4444-4004-4-40040000000000000000000000000000000000000000000000−22220000
χ654-4-4-4444-400-44400-40000000000000000000000000000000000000000000000002i2−2i200
χ664-4-4-4444-400-44400-4000000000000000000000000000000000000000000000000−2i22i200
χ678-88-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-88-88-88000000000000000000000000000000000000000000000000000000000000

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