Finite Group Databasebeta

← Group #291596

Character table — Group #291596

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444488888888888888888888888888888161616161616161616163232
order12222222444444442244444444444444444448888888888888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-11-11-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111
χ5111111111111111111111111-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ7111111111111111111111111-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111
χ8111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-1-1-11111-1-1
χ91111111111111111-1-1-1-1-1-11111-1-1-11111-1-1111111-1-1-1-11111-1-1-1-1-111-1-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-11111-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-11
χ121111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-111-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111-1-11-1-111-1-1-11
χ141111111111111111-1-1-1-1-1-111-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11-1-11-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1111-1
χ161111111111111111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-11
χ1722222222222-2-2-22-22222-2-2-2-200-200000022-2-20000000000000000-202000000000
χ1822222222222-2-2-22-22222-2-2-2-200-2000000-2-222000000000000000020-2000000000
χ1922222222222-2-2-22-2-2-2-2-222-2-200200000022220000000000000000-20-2000000000
χ2022222222222-2-2-22-2-2-2-2-222-2-2002000000-2-2-2-20000000000000000202000000000
χ2122222222-2-2-2222-2222-2-222-2-222-2220000000000000000000000000-20-200000000
χ2222222222-2-2-2222-2222-2-222-2-2-2-2-2-2-2000000000000000000000000020200000000
χ2322222222-2-2-2222-22-2-222-2-2-2-2222-2-20000000000000000000000000-20200000000
χ2422222222-2-2-2222-22-2-222-2-2-2-2-2-2222000000000000000000000000020-200000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2220020022-2-20000000000000000000000002-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-22200200-2-222000000000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222200-20022-2-2000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222200-200-2-2220000000000000000000000002-2000000
χ29222-22-2-2-20002-2-2022-2002-2002-202-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ30222-22-2-2-20002-2-2022-2002-2002-202-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ31222-22-2-2-20002-2-2022-2002-200-220-2200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ32222-22-2-2-20002-2-2022-2002-200-220-2200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ33222-22-2-2-20002-2-202-2200-22002-20-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ34222-22-2-2-20002-2-202-2200-22002-20-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ35222-22-2-2-20002-2-202-2200-2200-2202-200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ36222-22-2-2-20002-2-202-2200-2200-2202-200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ372-222-22-2-222-2-22-2-220000002-2000002i−2i2i−2i00002i−2i2i−2i0000000000000000002-20000
χ382-222-22-2-222-2-22-2-220000002-2000002i−2i2i−2i0000−2i2i−2i2i000000000000000000-220000
χ392-222-22-2-222-2-22-2-220000002-200000−2i2i−2i2i00002i−2i2i−2i000000000000000000-220000
χ402-222-22-2-222-2-22-2-220000002-200000−2i2i−2i2i0000−2i2i−2i2i0000000000000000002-20000
χ412-222-22-2-2-2-222-222-20000002-2000002i−2i−2i2i000000002-22-200000000000000002i−2i00
χ422-222-22-2-2-2-222-222-20000002-2000002i−2i−2i2i00000000-22-220000000000000000−2i2i00
χ432-222-22-2-2-2-222-222-20000002-200000−2i2i2i−2i000000002-22-20000000000000000−2i2i00
χ442-222-22-2-2-2-222-222-20000002-200000−2i2i2i−2i00000000-22-2200000000000000002i−2i00
χ45444-44-4-4-4000-4440-44-400-440000000000000000000000000000000000000000000
χ46444-44-4-4-4000-4440-4-44004-40000000000000000000000000000000000000000000
χ4744-44-4-44-44-44000-400000000000000000000000000000022−2222−220000000000000000
χ4844-44-4-44-44-44000-4000000000000000000000000000000−2222−22220000000000000000
χ4944-44-4-44-4-44-4000400000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ5044-44-4-44-4-44-400040000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ5144-4-4-44-4400000000004i−4i00000000000000000000000002i−2i−2i2i2-2-22000000000000
χ5244-4-4-44-4400000000004i−4i0000000000000000000000000−2i2i2i−2i-222-2000000000000
χ5344-4-4-44-440000000000−4i4i00000000000000000000000002i−2i−2i2i-222-2000000000000
χ5444-4-4-44-440000000000−4i4i0000000000000000000000000−2i2i2i−2i2-2-22000000000000
χ554-444-44-4-444-44-44-4-4000000-4400000000000000000000000000000000000000000
χ564-444-44-4-4-4-44-44-444000000-4400000000000000000000000000000000000000000
χ574-44-4-4-44400044-40-400000000000000000000000002i2−2i2−2i22i200000000000000000000
χ584-44-4-4-44400044-40-40000000000000000000000000−2i22i22i2−2i200000000000000000000
χ594-44-4-4-444000-4-440400000000000000000000022−22−2222000000000000000000000000
χ604-44-4-4-444000-4-4404000000000000000000000−222222−22000000000000000000000000
χ614-4-444-4-444-4-40004000000000000000000004-40000000000000000000000000000
χ624-4-444-4-444-4-4000400000000000000000000-440000000000000000000000000000
χ634-4-444-4-44-444000-40000000000000000004i−4i000000000000000000000000000000
χ644-4-444-4-44-444000-4000000000000000000−4i4i000000000000000000000000000000
χ658-8-8-8888-8000000000000000000000000000000000000000000000000000000000

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