Finite Group Databasebeta

← Group #305354

Character table — Group #305354

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-111-1-1-1-11111111111-1-1-1-1-1-1-11-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111-1-11111-1-1-111-1
χ911111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-111-1-11-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1111111-1-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-11111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111111111111-1-1-1-11-1-1-1-11
χ172222222222-2-22-2-22-200002222-222220000-2-2000022000000-2-200000000-2000000000000
χ182222222222-2-22-2-22-200002222-2-2-2-2-20000-2-20000-2-200000022000000002000000000000
χ192222222222-2-22-2-22-20000-2-2-2-2-222220000220000-2-2000000-2-2000000002000000000000
χ202222222222-2-22-2-22-20000-2-2-2-2-2-2-2-2-20000220000220000002200000000-2000000000000
χ2122222222-2-222-222-2-222220000-2000022220022-2-200-2-2000000000000000000000-200000
χ2222222222-2-222-222-2-222220000-20000-2-2-2-200-2-2-2-20022000000000000000000000200000
χ2322222222-2-222-222-2-2-2-2-2-20000-20000222200-2-22200-2-2000000000000000000000200000
χ2422222222-2-222-222-2-2-2-2-2-20000-20000-2-2-2-20022220022000000000000000000000-200000
χ2522-2-22-22-22-200-2002000002i2i−2i−2i02i2i−2i−2i22−2−20000002-22−2i2i2−i2−i2000000i2i2−i2−i2000000002−2000
χ2622-2-22-22-22-200-2002000002i2i−2i−2i02i2i−2i−2i−2−2220000002-2−22−i2−i2i2i2000000−i2−i2i2i200000000−22000
χ2722-2-22-22-22-200-2002000002i2i−2i−2i0−2i−2i2i2i22−2−2000000-222−2i2i2−i2−i2000000−i2−i2i2i200000000−22000
χ2822-2-22-22-22-200-2002000002i2i−2i−2i0−2i−2i2i2i−2−222000000-22−22−i2−i2i2i2000000i2i2−i2−i2000000002−2000
χ2922-2-22-22-22-200-200200000−2i−2i2i2i02i2i−2i−2i22−2−2000000-222−2−i2−i2i2i2000000i2i2−i2−i200000000−22000
χ3022-2-22-22-22-200-200200000−2i−2i2i2i02i2i−2i−2i−2−222000000-22−22i2i2−i2−i2000000−i2−i2i2i2000000002−2000
χ3122-2-22-22-22-200-200200000−2i−2i2i2i0−2i−2i2i2i22−2−20000002-22−2−i2−i2i2i2000000−i2−i2i2i2000000002−2000
χ3222-2-22-22-22-200-200200000−2i−2i2i2i0−2i−2i2i2i−2−2220000002-2−22i2i2−i2−i2000000i2i2−i2−i200000000−22000
χ3322-2-2-22-22002-202-2002i2i−2i−2i00000i2−i2i2−i22-22-2002i−2i0000000000i2−i222−2−2i2−i2i2−i200000000002−20
χ3422-2-2-22-22002-202-2002i2i−2i−2i00000i2−i2i2−i2-22-2200−2i2i0000000000i2−i222−2−2−i2i2−i2i20000000000−220
χ3522-2-2-22-22002-202-2002i2i−2i−2i00000−i2i2−i2i22-22-2002i−2i0000000000−i2i2−2−222−i2i2−i2i20000000000−220
χ3622-2-2-22-22002-202-2002i2i−2i−2i00000−i2i2−i2i2-22-2200−2i2i0000000000−i2i2−2−222i2−i2i2−i200000000002−20
χ3722-2-2-22-22002-202-200−2i−2i2i2i00000i2−i2i2−i22-22-200−2i2i0000000000i2−i2−2−222i2−i2i2−i20000000000−220
χ3822-2-2-22-22002-202-200−2i−2i2i2i00000i2−i2i2−i2-22-22002i−2i0000000000i2−i2−2−222−i2i2−i2i200000000002−20
χ3922-2-2-22-22002-202-200−2i−2i2i2i00000−i2i2−i2i22-22-200−2i2i0000000000−i2i222−2−2−i2i2−i2i200000000002−20
χ4022-2-2-22-22002-202-200−2i−2i2i2i00000−i2i2−i2i2-22-22002i−2i0000000000−i2i222−2−2i2−i2i2−i20000000000−220
χ412-22-222-2-22222-2-2-2-222-22-22-22-2-2000000002-2002-200000000000000000002-20000000000
χ422-22-222-2-22222-2-2-2-222-22-2-22-22-200000000-22002-20000000000000000000-220000000000
χ432-22-222-2-22222-2-2-2-22-22-222-22-2-2000000002-200-220000000000000000000-220000000000
χ442-22-222-2-22222-2-2-2-22-22-22-22-22-200000000-2200-2200000000000000000002-20000000000
χ452-22-222-2-222-2-2-222-2-200002-22-2200000000-22000000000000002i−2i2i−2i0000000002i−2i000000
χ462-22-222-2-222-2-2-222-2-200002-22-2200000000-2200000000000000−2i2i−2i2i000000000−2i2i000000
χ472-22-222-2-222-2-2-222-2-20000-22-222000000002-2000000000000002i−2i2i−2i000000000−2i2i000000
χ482-22-222-2-222-2-2-222-2-20000-22-222000000002-200000000000000−2i2i−2i2i0000000002i−2i000000
χ492-22-222-2-2-2-2222-2-22-22-22-200002000000000000-2200002i−2i2i−2i00000000000002i−2i00000000
χ502-22-222-2-2-2-2222-2-22-22-22-200002000000000000-220000−2i2i−2i2i0000000000000−2i2i00000000
χ512-22-222-2-2-2-2222-2-22-2-22-22000020000000000002-200002i−2i2i−2i0000000000000−2i2i00000000
χ522-22-222-2-2-2-2222-2-22-2-22-22000020000000000002-20000−2i2i−2i2i00000000000002i−2i00000000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ544444-4-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ554444-4-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ564444-4-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ574444-4-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ5844-4-44-44-4-4400400-4000000000000002222−22−2200000000−2222000000000000000000000000000
χ5944-4-44-44-4-4400400-400000000000000−22−2222220000000022−22000000000000000000000000000
χ6044-4-4-44-4400-440-44000000000002i2−2i22i2−2i2000000000000000000−2i22i2000000000000000000000
χ6144-4-4-44-4400-440-4400000000000−2i22i2−2i22i20000000000000000002i2−2i2000000000000000000000
χ624-44-444-4-4-4-4-4-44444400000000-4000000000000000000000000000000000000000000000
χ634-4-444-4-444-400400-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ644-4-444-4-444-400400-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ654-4-444-4-44-4400-4004000000000000000000000000000022−22−222200000000000000000000000
χ664-4-444-4-44-4400-40040000000000000000000000000000−222222−2200000000000000000000000
χ674-4-44-444-4004-40-44004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ684-4-44-444-4004-40-4400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4-44-444-400-4404-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ704-4-44-444-400-4404-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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