Finite Group Databasebeta

← Group #307991

Character table — Group #307991

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-111-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-1-111-1-1-1
χ911111111111111111-1-1-1-1111111111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-111-1-1111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-11111-1-1111111-1-1-1-1-111-1-1-1-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-11-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1111111-1-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-11111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11-1-11111-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111111111-1-1-1-1111-1-1-1-11
χ172222222222-2-2-222-2-222220000-2000022220022-2-200000000-2-2000000000000000-200000
χ182222222222-2-2-222-2-222220000-20000-2-2-2-200-2-2-2-20000000022000000000000000200000
χ192222222222-2-2-222-2-2-2-2-2-20000-20000222200-2-22200000000-2-2000000000000000200000
χ202222222222-2-2-222-2-2-2-2-2-20000-20000-2-2-2-20022220000000022000000000000000-200000
χ2122222222-2-2222-2-22-200002222-222220000-2-20000220000-2-20000000000-2000000000000
χ2222222222-2-2222-2-22-200002222-2-2-2-2-20000-2-20000-2-200002200000000002000000000000
χ2322222222-2-2222-2-22-20000-2-2-2-2-222220000220000-2-20000-2-200000000002000000000000
χ2422222222-2-2222-2-22-20000-2-2-2-2-2-2-2-2-20000220000220000220000000000-2000000000000
χ2522-22-22-2-2222-22-2-2-22000022-2-2-2000000002-200000022-2-200000000000002-20000000000
χ2622-22-22-2-2222-22-2-2-22000022-2-2-2000000002-2000000-2-2220000000000000-220000000000
χ2722-22-22-2-2222-22-2-2-220000-2-222-200000000-2200000022-2-20000000000000-220000000000
χ2822-22-22-2-2222-22-2-2-220000-2-222-200000000-22000000-2-22200000000000002-20000000000
χ2922-22-22-2-2-2-22-2222-2-22i2i−2i−2i22-2-2200000000-22002i−2i000000000000000000000002i−2i000000
χ3022-22-22-2-2-2-22-2222-2-22i2i−2i−2i-2-2222000000002-2002i−2i00000000000000000000000−2i2i000000
χ3122-22-22-2-2-2-22-2222-2-2−2i−2i2i2i22-2-2200000000-2200−2i2i00000000000000000000000−2i2i000000
χ3222-22-22-2-2-2-22-2222-2-2−2i−2i2i2i-2-2222000000002-200−2i2i000000000000000000000002i−2i000000
χ3322-22-22-2-2-2-2-22-222222i2i−2i−2i0000-2000000000000−2i2i000000000022-2-200000002i−2i00000000
χ3422-22-22-2-2-2-2-22-222222i2i−2i−2i0000-2000000000000−2i2i0000000000-2-2220000000−2i2i00000000
χ3522-22-22-2-2-2-2-22-22222−2i−2i2i2i0000-20000000000002i−2i000000000022-2-20000000−2i2i00000000
χ3622-22-22-2-2-2-2-22-22222−2i−2i2i2i0000-20000000000002i−2i0000000000-2-22200000002i−2i00000000
χ372-222-2-2-222-20002-2002-22-200000i2i2−i2−i22i2i−2i−2i002i−2i0000i2−i2i2−i2i2−i200000022−2−2000000002−2000
χ382-222-2-2-222-20002-2002-22-200000i2i2−i2−i2−2i−2i2i2i00−2i2i0000i2−i2i2−i2i2−i2000000−2−22200000000−22000
χ392-222-2-2-222-20002-2002-22-200000−i2−i2i2i22i2i−2i−2i002i−2i0000−i2i2−i2i2−i2i2000000−2−22200000000−22000
χ402-222-2-2-222-20002-2002-22-200000−i2−i2i2i2−2i−2i2i2i00−2i2i0000−i2i2−i2i2−i2i200000022−2−2000000002−2000
χ412-222-2-2-222-20002-200-22-2200000i2i2−i2−i22i2i−2i−2i00−2i2i0000−i2i2−i2i2i2−i200000022−2−200000000−22000
χ422-222-2-2-222-20002-200-22-2200000i2i2−i2−i2−2i−2i2i2i002i−2i0000−i2i2−i2i2i2−i2000000−2−222000000002−2000
χ432-222-2-2-222-20002-200-22-2200000−i2−i2i2i22i2i−2i−2i00−2i2i0000i2−i2i2−i2−i2i2000000−2−222000000002−2000
χ442-222-2-2-222-20002-200-22-2200000−i2−i2i2i2−2i−2i2i2i002i−2i0000i2−i2i2−i2−i2i200000022−2−200000000−22000
χ452-22-2-222-2002-2-2002000002i−2i2i−2i02i−2i2i−2ii2−i2i2−i20000002-2000000i2−i22−22−22−22−20000000000i2−i20
χ462-22-2-222-2002-2-2002000002i−2i2i−2i02i−2i2i−2i−i2i2−i2i20000002-2000000−i2i2−22−22−22−220000000000−i2i20
χ472-22-2-222-2002-2-2002000002i−2i2i−2i0−2i2i−2i2ii2−i2i2−i2000000-22000000i2−i22−22−2−22−220000000000−i2i20
χ482-22-2-222-2002-2-2002000002i−2i2i−2i0−2i2i−2i2i−i2i2−i2i2000000-22000000−i2i2−22−222−22−20000000000i2−i20
χ492-22-2-222-2002-2-200200000−2i2i−2i2i02i−2i2i−2ii2−i2i2−i2000000-22000000i2−i2−22−222−22−20000000000−i2i20
χ502-22-2-222-2002-2-200200000−2i2i−2i2i02i−2i2i−2i−i2i2−i2i2000000-22000000−i2i22−22−2−22−220000000000i2−i20
χ512-22-2-222-2002-2-200200000−2i2i−2i2i0−2i2i−2i2ii2−i2i2−i20000002-2000000i2−i2−22−22−22−220000000000i2−i20
χ522-22-2-222-2002-2-200200000−2i2i−2i2i0−2i2i−2i2i−i2i2−i2i20000002-2000000−i2i22−22−22−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-44-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ55444-44-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ56444-44-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ57444-44-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ5844-44-44-4-444-44-4-4-44-4000000004000000000000000000000000000000000000000000000
χ594-444-4-4-44-44000-44000000000002i22i2−2i2−2i20000000000000000−2i22i200000000000000000000000
χ604-444-4-4-44-44000-4400000000000−2i2−2i22i22i200000000000000002i2−2i200000000000000000000000
χ614-44-4-444-400-44400-4000000000000002i2−2i22i2−2i200000000000000−2i22i2000000000000000000000
χ624-44-4-444-400-44400-400000000000000−2i22i2−2i22i2000000000000002i2−2i2000000000000000000000
χ634-4-444-44-44-4000-440000000000000000000000000002i2−2i2−2i22i20000000000000000000000000
χ644-4-444-44-44-4000-44000000000000000000000000000−2i22i22i2−2i20000000000000000000000000
χ654-4-444-44-4-440004-4004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ664-4-444-44-4-440004-400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ674-4-4-444-440044-400-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ684-4-4-444-440044-400-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ694-4-4-444-4400-4-44004000000000000000000000000000000000022−22−222200000000000000000
χ704-4-4-444-4400-4-440040000000000000000000000000000000000−222222−2200000000000000000
χ7188-8-8-8-888000000000000000000000000000000000000000000000000000000000000000

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