Finite Group Databasebeta

← Group #307995

Character table — Group #307995

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-11-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-11-1-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111111-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111111111-1-1-1-11111-1-1-1-11
χ17222222222-2-2222-2-2-222220000-200002222-2-2000022-2-200000000000000000000-2000000
χ18222222222-2-2222-2-2-222220000-20000-2-2-2-2-2-20000-2-222000000000000000000002000000
χ19222222222-2-2222-2-2-2-2-2-2-20000-200002222220000-2-2-2-2000000000000000000002000000
χ20222222222-2-2222-2-2-2-2-2-2-20000-20000-2-2-2-2220000222200000000000000000000-2000000
χ2122222222-222-2-2-222-200002222-22222000000-2-22200000000-2-2000000000000000-200000
χ2222222222-222-2-2-222-200002222-2-2-2-2-2000000-2-2-2-20000000022000000000000000200000
χ2322222222-222-2-2-222-20000-2-2-2-2-2222200000022-2-200000000-2-2000000000000000200000
χ2422222222-222-2-2-222-20000-2-2-2-2-2-2-2-2-200000022220000000022000000000000000-200000
χ252222-2-2-2-2222-22-2-2-2222-2-20000-2000000002-20000000022-2-200000000002-200000000000
χ262222-2-2-2-2222-22-2-2-2222-2-20000-2000000002-200000000-2-2220000000000-2200000000000
χ272222-2-2-2-2222-22-2-2-22-2-2220000-200000000-220000000022-2-20000000000-2200000000000
χ282222-2-2-2-2222-22-2-2-22-2-2220000-200000000-2200000000-2-22200000000002-200000000000
χ292222-2-2-2-22-2-2-22-222-222-2-22i2i−2i−2i200000000-222i−2i0000000000000000000000002i−2i0000000
χ302222-2-2-2-22-2-2-22-222-222-2-2−2i−2i2i2i200000000-22−2i2i000000000000000000000000−2i2i0000000
χ312222-2-2-2-22-2-2-22-222-2-2-2222i2i−2i−2i2000000002-22i−2i000000000000000000000000−2i2i0000000
χ322222-2-2-2-22-2-2-22-222-2-2-222−2i−2i2i2i2000000002-2−2i2i0000000000000000000000002i−2i0000000
χ332222-2-2-2-2-2-2-22-2222200002i2i−2i−2i-20000000000−2i2i00000000000022-2-20000002i−2i000000000
χ342222-2-2-2-2-2-2-22-2222200002i2i−2i−2i-20000000000−2i2i000000000000-2-222000000−2i2i000000000
χ352222-2-2-2-2-2-2-22-222220000−2i−2i2i2i-200000000002i−2i00000000000022-2-2000000−2i2i000000000
χ362222-2-2-2-2-2-2-22-222220000−2i−2i2i2i-200000000002i−2i000000000000-2-2220000002i−2i000000000
χ3722-2-22-2-222002-2-20002i−2i2i−2i0000022−2−22i2i−2i−2i0000002-20000002−2i2−i2i2−i2i2i2−i2−i2000000002−2000
χ3822-2-22-2-222002-2-20002i−2i2i−2i0000022−2−2−2i−2i2i2i000000-220000002−2i2−i2i2−i2−i2−i2i2i200000000−22000
χ3922-2-22-2-222002-2-20002i−2i2i−2i00000−2−2222i2i−2i−2i0000002-2000000−22−i2i2−i2i2−i2−i2i2i200000000−22000
χ4022-2-22-2-222002-2-20002i−2i2i−2i00000−2−222−2i−2i2i2i000000-22000000−22−i2i2−i2i2i2i2−i2−i2000000002−2000
χ4122-2-22-2-222002-2-2000−2i2i−2i2i0000022−2−22i2i−2i−2i000000-220000002−2−i2i2−i2i2i2i2−i2−i200000000−22000
χ4222-2-22-2-222002-2-2000−2i2i−2i2i0000022−2−2−2i−2i2i2i0000002-20000002−2−i2i2−i2i2−i2−i2i2i2000000002−2000
χ4322-2-22-2-222002-2-2000−2i2i−2i2i00000−2−2222i2i−2i−2i000000-22000000−22i2−i2i2−i2−i2−i2i2i2000000002−2000
χ4422-2-22-2-222002-2-2000−2i2i−2i2i00000−2−222−2i−2i2i2i0000002-2000000−22i2−i2i2−i2i2i2−i2−i200000000−22000
χ452-2-2222-2-202-20002-2000002i−2i2i−2i02i−2i2i−2ii2−i2i2−i200002-200i2−i22−22−20000002−22−20000000000i2−i20
χ462-2-2222-2-202-20002-2000002i−2i2i−2i02i−2i2i−2i−i2i2−i2i200002-200−i2i2−22−22000000−22−220000000000−i2i20
χ472-2-2222-2-202-20002-2000002i−2i2i−2i0−2i2i−2i2ii2−i2i2−i20000-2200i2−i22−22−2000000−22−220000000000−i2i20
χ482-2-2222-2-202-20002-2000002i−2i2i−2i0−2i2i−2i2i−i2i2−i2i20000-2200−i2i2−22−220000002−22−20000000000i2−i20
χ492-2-2222-2-202-20002-200000−2i2i−2i2i02i−2i2i−2ii2−i2i2−i20000-2200i2−i2−22−220000002−22−20000000000−i2i20
χ502-2-2222-2-202-20002-200000−2i2i−2i2i02i−2i2i−2i−i2i2−i2i20000-2200−i2i22−22−2000000−22−220000000000i2−i20
χ512-2-2222-2-202-20002-200000−2i2i−2i2i0−2i2i−2i2ii2−i2i2−i200002-200i2−i2−22−22000000−22−220000000000i2−i20
χ522-2-2222-2-202-20002-200000−2i2i−2i2i0−2i2i−2i2i−i2i2−i2i200002-200−i2i22−22−20000002−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4444-44-4-4-4000000004000000000000000000000000000000000000000000000
χ5544-4-44-4-44-400-4440000000000002222−22−22000000000000000000−2222000000000000000000000
χ5644-4-44-4-44-400-444000000000000−22−22222200000000000000000022−22000000000000000000000
χ5744-4-4-444-4400-4-440004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ5844-4-4-444-4400-4-44000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ5944-4-4-444-4-40044-40000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ6044-4-4-444-4-40044-4000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ614-44-44-44-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ624-44-44-44-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ634-44-44-44-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ644-44-44-44-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ654-4-4444-4-40-44000-44000000000000002i2−2i22i2−2i200000000−2i22i2000000000000000000000000000
χ664-4-4444-4-40-44000-4400000000000000−2i22i2−2i22i2000000002i2−2i2000000000000000000000000000
χ674-4-44-4-44404-4000-44000000000000000000000000000022−22−222200000000000000000000000
χ684-4-44-4-44404-4000-440000000000000000000000000000−222222−2200000000000000000000000
χ694-4-44-4-4440-440004-4000004-4-440000000000000000000000000000000000000000000000
χ704-4-44-4-4440-440004-400000-444-40000000000000000000000000000000000000000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

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