Finite Group Databasebeta

← Group #305756

Character table — Group #305756

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-11111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1111111-1-1-1
χ911111111111111111-1-1-1-1111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11
χ1011111111111111111-1-1-1-1111111111-1-111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1111-1-111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-111-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11-11111-1-111-1-111-1
χ172222222222-2-2-222-2-20000-22222222200-2-20000-2-20000000000-200000000000000
χ182222222222-2-2-222-2-20000-22222-2-2-2-200220000-2-20000000000200000000000000
χ192222222222-2-2-222-2-20000-2-2-2-2-222-2-200-2-20000220000000000200000000000000
χ202222222222-2-2-222-2-20000-2-2-2-2-2-2-22200220000220000000000-200000000000000
χ2122222222-2-2222-2-22-22222-200000000-2-20022-2-20000002200000-20000000000000
χ2222222222-2-2222-2-22-22222-200000000-2-200-2-222000000-2-20000020000000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-20000000022002222000000-2-200000-20000000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2000000002200-2-2-2-2000000220000020000000000000
χ2522-2-2-222-22222-2-2-2-2222-2-2-200002-2002-22-2000000000000000000002-2000000000
χ2622-2-2-222-22222-2-2-2-2222-2-2-20000-22002-2-2200000000000000000000-22000000000
χ2722-2-2-222-22222-2-2-2-22-2-222-200002-200-222-200000000000000000000-22000000000
χ2822-2-2-222-22222-2-2-2-22-2-222-20000-2200-22-22000000000000000000002-2000000000
χ2922-2-2-222-222-2-22-2-22-20000200002-20000-220000002i2i−2i−2i0000000000002i−2i0000000
χ3022-2-2-222-222-2-22-2-22-20000200002-20000-22000000−2i−2i2i2i000000000000−2i2i0000000
χ3122-2-2-222-222-2-22-2-22-2000020000-2200002-20000002i2i−2i−2i000000000000−2i2i0000000
χ3222-2-2-222-222-2-22-2-22-2000020000-2200002-2000000−2i−2i2i2i0000000000002i−2i0000000
χ3322-2-2-222-2-2-222-222-2-222-2-2200000000-22000000000000000000002i−2i0000002i−2i000
χ3422-2-2-222-2-2-222-222-2-222-2-2200000000-2200000000000000000000−2i2i000000−2i2i000
χ3522-2-2-222-2-2-222-222-2-2-2-2222000000002-2000000000000000000002i−2i000000−2i2i000
χ3622-2-2-222-2-2-222-222-2-2-2-2222000000002-200000000000000000000−2i2i0000002i−2i000
χ372-222-22-2-2002-2-200202i−2i2i−2i022−2−2000000002i−2i002−2i2−i2i2−i22-222−2−200000000i2−i200000
χ382-222-22-2-2002-2-200202i−2i2i−2i022−2−200000000−2i2i002−2i2−i2i2−i2-22−2−22200000000−i2i200000
χ392-222-22-2-2002-2-200202i−2i2i−2i0−2−222000000002i−2i00−22−i2i2−i2i22-2−2−22200000000−i2i200000
χ402-222-22-2-2002-2-200202i−2i2i−2i0−2−22200000000−2i2i00−22−i2i2−i2i2-2222−2−200000000i2−i200000
χ412-222-22-2-2002-2-20020−2i2i−2i2i022−2−2000000002i−2i002−2−i2i2−i2i2-22−2−22200000000i2−i200000
χ422-222-22-2-2002-2-20020−2i2i−2i2i022−2−200000000−2i2i002−2−i2i2−i2i22-222−2−200000000−i2i200000
χ432-222-22-2-2002-2-20020−2i2i−2i2i0−2−222000000002i−2i00−22i2−i2i2−i2-2222−2−200000000−i2i200000
χ442-222-22-2-2002-2-20020−2i2i−2i2i0−2−22200000000−2i2i00−22i2−i2i2−i22-2−2−22200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-44-40004-400000000000004-400000000000000000000000000000000000
χ47444-44-4-4-44-40004-40000000000000-4400000000000000000000000000000000000
χ48444-44-4-4-4-44000-440000000000000000000000000000000000000000000000022−220
χ49444-44-4-4-4-44000-4400000000000000000000000000000000000000000000000−22220
χ5044-44-4-4-444-4000-4400000004i−4i4i−4i000000000000000000000000000000000000000
χ5144-44-4-4-444-4000-440000000−4i4i−4i4i000000000000000000000000000000000000000
χ5244-44-4-4-44-440004-400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ5344-44-4-4-44-440004-40000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ5444-4-4-444-4-4-4-4-4444440000-40000000000000000000000000000000000000000000
χ554-444-44-4-400-44400-40000002222−22−22000000000000−22220000000000000000000000000
χ564-444-44-4-400-44400-4000000−22−22222200000000000022−220000000000000000000000000
χ574-4-444-44-4000000000000002i2−2i2−2i22i2000000000022−22000000002i−2i−2i2i000000000000000
χ584-4-444-44-4000000000000002i2−2i2−2i22i20000000000−222200000000−2i2i2i−2i000000000000000
χ594-4-444-44-400000000000000−2i22i22i2−2i2000000000022−2200000000−2i2i2i−2i000000000000000
χ604-4-444-44-400000000000000−2i22i22i2−2i20000000000−2222000000002i−2i−2i2i000000000000000
χ614-4-4-444-44004-4400-404i−4i−4i4i00000000000000000000000000000000000000000000
χ624-4-4-444-44004-4400-40−4i4i4i−4i00000000000000000000000000000000000000000000
χ634-4-4-444-4400-44-400400000000000000000000000022−22−2222000000000000000000000
χ644-4-4-444-4400-44-4004000000000000000000000000−222222−22000000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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