Finite Group Databasebeta

← Group #350170

Character table — Group #350170

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442244444444444444222244444444444444444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-1-1-1-1-11111-1-1-1-1111111-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-11111-1-1-1-1111111-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ172222222222-2-222-2-22222-2-200000000-2-20000-22200000000-2-222-2-2000000000000000000
χ182222222222-2-222-2-22222-2-200000000-2-20000-2-2-20000000022-2-222000000000000000000
χ192222222222-2-222-2-2-2-2-2-22200000000-2-2000022200000000-2-2-2-222000000000000000000
χ202222222222-2-222-2-2-2-2-2-22200000000-2-200002-2-2000000002222-2-2000000000000000000
χ2122222222-2-222-2-22222-2-2-2-22222-2-2-2-2-2-20000200-2-2220000000000000000000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-2000020022-2-20000000000000000000000000000
χ2322222222-2-222-2-222-2-2222222222222-2-20000-200-2-2-2-20000000000000000000000000000
χ2422222222-2-222-2-222-2-22222-2-2-2-2-2-2-2-2-2-20000-20022220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222000000002222-2-2-200000022-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2220000000022-2-222-2000000-2-222000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2000000002222-2-22000000-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-20000000022-2-222200000022-2-2000000000000000000000000
χ29222-22-2-2-2002-2002-2002i−2i2i−2i22-2-22i2i−2i−2i0000000000000000000000022−2−2i2i2−i2−i22−2i2−i2000000
χ30222-22-2-2-2002-2002-2002i−2i2i−2i22-2-22i2i−2i−2i00000000000000000000000−2−222−i2−i2i2i2−22−i2i2000000
χ31222-22-2-2-2002-2002-2002i−2i2i−2i-2-222−2i−2i2i2i0000000000000000000000022−2−2i2i2−i2−i2−22−i2i2000000
χ32222-22-2-2-2002-2002-2002i−2i2i−2i-2-222−2i−2i2i2i00000000000000000000000−2−222−i2−i2i2i22−2i2−i2000000
χ33222-22-2-2-2002-2002-200−2i2i−2i2i22-2-2−2i−2i2i2i0000000000000000000000022−2−2−i2−i2i2i22−2−i2i2000000
χ34222-22-2-2-2002-2002-200−2i2i−2i2i22-2-2−2i−2i2i2i00000000000000000000000−2−222i2i2−i2−i2−22i2−i2000000
χ35222-22-2-2-2002-2002-200−2i2i−2i2i-2-2222i2i−2i−2i0000000000000000000000022−2−2−i2−i2i2i2−22i2−i2000000
χ36222-22-2-2-2002-2002-200−2i2i−2i2i-2-2222i2i−2i−2i00000000000000000000000−2−222i2i2−i2−i22−2−i2i2000000
χ3722-22-22-2-22-22-22-2-220000002i−2i2i−2i00002-200000002i−2i002-22-2002i−2i2i−2i000000000000000000
χ3822-22-22-2-22-22-22-2-220000002i−2i2i−2i00002-200000002i−2i00-22-2200−2i2i−2i2i000000000000000000
χ3922-22-22-2-22-22-22-2-22000000−2i2i−2i2i00002-20000000−2i2i002-22-200−2i2i−2i2i000000000000000000
χ4022-22-22-2-22-22-22-2-22000000−2i2i−2i2i00002-20000000−2i2i00-22-22002i−2i2i−2i000000000000000000
χ4122-22-22-2-22-2-222-22-200000000002i−2i2i−2i-222-22-2000002i−2i0000002i−2i−2i2i000000000000000000
χ4222-22-22-2-22-2-222-22-200000000002i−2i2i−2i-22-22-22000002i−2i000000−2i2i2i−2i000000000000000000
χ4322-22-22-2-22-2-222-22-20000000000−2i2i−2i2i-222-22-200000−2i2i000000−2i2i2i−2i000000000000000000
χ4422-22-22-2-22-2-222-22-20000000000−2i2i−2i2i-22-22-2200000−2i2i0000002i−2i−2i2i000000000000000000
χ4522-22-22-2-2-222-2-22-220000002i−2i2i−2i0000-222-2-2202i−2i−2i2i0000002i−2i0000000000000000000000
χ4622-22-22-2-2-222-2-22-220000002i−2i2i−2i0000-22-222-20−2i2i−2i2i000000−2i2i0000000000000000000000
χ4722-22-22-2-2-222-2-22-22000000−2i2i−2i2i0000-222-2-220−2i2i2i−2i000000−2i2i0000000000000000000000
χ4822-22-22-2-2-222-2-22-22000000−2i2i−2i2i0000-22-222-202i−2i2i−2i0000002i−2i0000000000000000000000
χ4922-22-22-2-2-22-22-222-200000000002i−2i2i−2i2-2000002i−2i00−2i2i-222-2−2i2i0000000000000000000000
χ5022-22-22-2-2-22-22-222-200000000002i−2i2i−2i2-200000−2i2i00−2i2i2-2-222i−2i0000000000000000000000
χ5122-22-22-2-2-22-22-222-20000000000−2i2i−2i2i2-2000002i−2i002i−2i2-2-22−2i2i0000000000000000000000
χ5222-22-22-2-2-22-22-222-20000000000−2i2i−2i2i2-200000−2i2i002i−2i-222-22i−2i0000000000000000000000
χ53444-44-4-4-400-4400-44004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ54444-44-4-4-400-4400-4400−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ5544-4-4-4-444004400-4-40000004i−4i−4i4i000000000000000000000000000000000000000000000
χ5644-4-4-4-444004400-4-4000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ5744-4-4-4-44400-4-4004400000000004-4-4400000000000000000000000000000000000000000
χ5844-4-4-4-44400-4-400440000000000-444-400000000000000000000000000000000000000000
χ594-444-4-44-44-400-440000000000000000000000000000000000000000000000000002i2−2i20000
χ604-444-4-44-44-400-44000000000000000000000000000000000000000000000000000−2i22i20000
χ614-444-4-44-4-44004-4000000000000000000000000000000000000000000000000000002i2−2i200
χ624-444-4-44-4-44004-400000000000000000000000000000000000000000000000000000−2i22i200
χ634-4-444-4-444400-4-400000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ644-4-444-4-444400-4-40000000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ654-4-444-4-44-4-4004400000000000000000000000000000000000000022−2222−2200000000000000
χ664-4-444-4-44-4-40044000000000000000000000000000000000000000−2222−222200000000000000
χ674-4-4-4444-4000000004-4000000000000000000000000000000000002-2-222-2-220000000000
χ684-4-4-4444-4000000004-400000000000000000000000000000000000-222-2-222-20000000000
χ694-4-4-4444-400000000-44000000000000000000000000000000000002-2-22-222-20000000000
χ704-4-4-4444-400000000-4400000000000000000000000000000000000-222-22-2-220000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

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