Finite Group Databasebeta

← Group #100618

Character table — Group #100618

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444488888888888888882488888888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-11-111-1-1-11-1-1111-1-1ii−i−iii−i−iiiii−i−i−i−i1-1i−ii−iii−i−i11-1-11-1
χ1011111111-1-1-1-11-111-1-1-11-1-1111-1-1ii−i−iii−i−i−i−i−i−iiiii1-1i−ii−i−i−iii-1-111-11
χ1111111111-1-1-1-11-111-1-1-11-1-1111-1-1−i−iii−i−iiiiiii−i−i−i−i1-1−ii−iiii−i−i-1-111-11
χ1211111111-1-1-1-11-111-1-1-11-1-1111-1-1−i−iii−i−iii−i−i−i−iiiii1-1−ii−ii−i−iii11-1-11-1
χ1311111111-1-1-1-11-111-1-1-11-1-11-1-111ii−i−i−i−iiiiiii−i−i−i−i-11i−i−ii−i−iii11-1-1-11
χ1411111111-1-1-1-11-111-1-1-11-1-11-1-111ii−i−i−i−iii−i−i−i−iiiii-11i−i−iiii−i−i-1-1111-1
χ1511111111-1-1-1-11-111-1-1-11-1-11-1-111−i−iiiii−i−iiiii−i−i−i−i-11−iii−i−i−iii-1-1111-1
χ1611111111-1-1-1-11-111-1-1-11-1-11-1-111−i−iiiii−i−i−i−i−i−iiiii-11−iii−iii−i−i11-1-1-11
χ172222222222222-2-2-2-2222-2-2-222220000000000000000-2-200000000000000
χ182222222222222-2-2-2-2222-2-2-2-2-2-2-200000000000000002200000000000000
χ19222222222222-22-2-2-2-2-2-22-22000000002222000000000000-2-20000000000
χ20222222222222-22-2-2-2-2-2-22-2200000000-2-2-2-2000000000000220000000000
χ21222222222222-2-2222-2-2-2-22-20000222200000000000000-2-2000000000000
χ22222222222222-2-2222-2-2-2-22-20000-2-2-2-20000000000000022000000000000
χ2322222222-2-2-2-222-2-22-2-2222-222-2-20000000000000000-2200000000000000
χ2422222222-2-2-2-222-2-22-2-2222-2-2-22200000000000000002-200000000000000
χ2522222222-2-2-2-2-2222-222-22-2-200002i2i−2i−2i00000000000000−2i2i000000000000
χ2622222222-2-2-2-2-2222-222-22-2-20000−2i−2i2i2i000000000000002i−2i000000000000
χ2722222222-2-2-2-2-2-2-2-2222-2-222000000002i2i−2i−2i000000000000−2i2i0000000000
χ2822222222-2-2-2-2-2-2-2-2222-2-22200000000−2i−2i2i2i0000000000002i−2i0000000000
χ2922-2-22-2-222-2-22200002-2-20002i−2i2i−2i0000000022−2−222−2−2000000i2−i2i2−i2000000
χ3022-2-22-2-222-2-22200002-2-20002i−2i2i−2i00000000−2−222−2−222000000−i2i2−i2i2000000
χ3122-2-22-2-222-2-22200002-2-2000−2i2i−2i2i0000000022−2−222−2−2000000−i2i2−i2i2000000
χ3222-2-22-2-222-2-22200002-2-2000−2i2i−2i2i00000000−2−222−2−222000000i2−i2i2−i2000000
χ3322-2-22-2-22-222-220000-22-20002i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i2000000−222−2000000
χ3422-2-22-2-22-222-220000-22-20002i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i20000002−2−22000000
χ3522-2-22-2-22-222-220000-22-2000−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i20000002−2−22000000
χ3622-2-22-2-22-222-220000-22-2000−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i2000000−222−2000000
χ372-2-2-2222-222-2-2002-2-200002000002i−2i2i−2i00002−22−22−22−20000000000i2−i2i2−i200
χ382-2-2-2222-222-2-2002-2-200002000002i−2i2i−2i0000−22−22−22−220000000000−i2i2−i2i200
χ392-2-2-2222-222-2-2002-2-20000200000−2i2i−2i2i00002−22−22−22−20000000000−i2i2−i2i200
χ402-2-2-2222-222-2-2002-2-20000200000−2i2i−2i2i0000−22−22−22−220000000000i2−i2i2−i200
χ412-2-2-2222-2-2-222002-220000-2000002-2-220000i2−i2i2−i2−i2i2−i2i20000000000−i2i2i2−i200
χ422-2-2-2222-2-2-222002-220000-2000002-2-220000−i2i2−i2i2i2−i2i2−i20000000000i2−i2−i2i200
χ432-2-2-2222-2-2-222002-220000-200000-222-20000i2−i2i2−i2−i2i2−i2i20000000000i2−i2−i2i200
χ442-2-2-2222-2-2-222002-220000-200000-222-20000−i2i2−i2i2i2−i2i2−i20000000000−i2i2i2−i200
χ4544-4-44-4-444-4-44-40000-444000000000000000000000000000000000000000
χ4644-4-44-4-44-444-4-400004-44000000000000000000000000000000000000000
χ474-4444-4-4-44-44-4000000000000000000000002-2-222-2-220000000000000000
χ484-4444-4-4-44-44-400000000000000000000000-222-2-222-20000000000000000
χ494-4444-4-4-4-44-44000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ504-4444-4-4-4-44-4400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ514-44-4-44-44000004000000-400000000002i2−2i22i2−2i2000000000000000000000000
χ524-44-4-44-44000004000000-40000000000−2i22i2−2i22i2000000000000000000000000
χ534-44-4-44-4400000-40000004000000000022−22−2222000000000000000000000000
χ544-44-4-44-4400000-400000040000000000−222222−22000000000000000000000000
χ554-4-4-4444-444-4-400-4440000-40000000000000000000000000000000000000
χ564-4-4-4444-4-4-44400-44-4000040000000000000000000000000000000000000
χ57888-8-8-88-8000000000000000000000000000000000000000000000000000
χ5888-88-88-8-8000000000000000000000000000000000000000000000000000
χ598-8-88-8-888000000000000000000000000000000000000000000000000000

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