Finite Group Databasebeta

← Group #310199

Character table — Group #310199

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
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
χ5111111111111111111111-1-1-1-111111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111-1-1-1-11111111111-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-111-1-1-111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111-1-111-111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111111-1-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111111111111-1-11-1-1-1-1-1-11
χ17222222222-222-2-2-22-222220000-200002222-2-2000022-2-200000000000000-2000000000000
χ18222222222-222-2-2-22-222220000-20000-2-2-2-2-2-20000-2-222000000000000002000000000000
χ19222222222-222-2-2-22-2-2-2-2-20000-200002222220000-2-2-2-2000000000000002000000000000
χ20222222222-222-2-2-22-2-2-2-2-20000-20000-2-2-2-2220000222200000000000000-2000000000000
χ2122222222-22-2-2222-2-200002222-2222200000022-2-200000000-2-20000000000000-20000000
χ2222222222-22-2-2222-2-200002222-2-2-2-2-2000000-2-2-2-20000000022000000000000020000000
χ2322222222-22-2-2222-2-20000-2-2-2-2-22222000000-2-22200000000-2-2000000000000020000000
χ2422222222-22-2-2222-2-20000-2-2-2-2-2-2-2-2-2000000222200000000220000000000000-20000000
χ2522-22-2-2-220-20022-20000002i2i−2i−2i022-2-2i2i2−i2−i2002i−2i0000i2−i200000022−2−2i2i2−i2−i200000000002−20
χ2622-22-2-2-220-20022-20000002i2i−2i−2i022-2-2−i2−i2i2i2002i−2i0000−i2i2000000−2−222−i2−i2i2i20000000000−220
χ2722-22-2-2-220-20022-20000002i2i−2i−2i0-2-222i2i2−i2−i200−2i2i0000i2−i200000022−2−2−i2−i2i2i20000000000−220
χ2822-22-2-2-220-20022-20000002i2i−2i−2i0-2-222−i2−i2i2i200−2i2i0000−i2i2000000−2−222i2i2−i2−i200000000002−20
χ2922-22-2-2-220-20022-2000000−2i−2i2i2i022-2-2i2i2−i2−i200−2i2i0000i2−i2000000−2−222i2i2−i2−i20000000000−220
χ3022-22-2-2-220-20022-2000000−2i−2i2i2i022-2-2−i2−i2i2i200−2i2i0000−i2i200000022−2−2−i2−i2i2i200000000002−20
χ3122-22-2-2-220-20022-2000000−2i−2i2i2i0-2-222i2i2−i2−i2002i−2i0000i2−i2000000−2−222−i2−i2i2i200000000002−20
χ3222-22-2-2-220-20022-2000000−2i−2i2i2i0-2-222−i2−i2i2i2002i−2i0000−i2i200000022−2−2i2i2−i2−i20000000000−220
χ3322-2-2-222-2-202-2000202i2i−2i−2i000002−22−22i−2i2i−2i0000002-200i2i2−i2−i22−20000i2−i2i2−i2000000002−2000
χ3422-2-2-222-2-202-2000202i2i−2i−2i000002−22−2−2i2i−2i2i000000-2200i2i2−i2−i22−20000−i2i2−i2i200000000−22000
χ3522-2-2-222-2-202-2000202i2i−2i−2i00000−22−222i−2i2i−2i0000002-200−i2−i2i2i2−220000−i2i2−i2i200000000−22000
χ3622-2-2-222-2-202-2000202i2i−2i−2i00000−22−22−2i2i−2i2i000000-2200−i2−i2i2i2−220000i2−i2i2−i2000000002−2000
χ3722-2-2-222-2-202-200020−2i−2i2i2i000002−22−22i−2i2i−2i000000-2200−i2−i2i2i22−20000i2−i2i2−i200000000−22000
χ3822-2-2-222-2-202-200020−2i−2i2i2i000002−22−2−2i2i−2i2i0000002-200−i2−i2i2i22−20000−i2i2−i2i2000000002−2000
χ3922-2-2-222-2-202-200020−2i−2i2i2i00000−22−222i−2i2i−2i000000-2200i2i2−i2−i2−220000−i2i2−i2i2000000002−2000
χ4022-2-2-222-2-202-200020−2i−2i2i2i00000−22−22−2i2i−2i2i0000002-200i2i2−i2−i2−220000i2−i2i2−i200000000−22000
χ412-22-2-22-2222-2-2-22-22200002i−2i2i−2i-20000000000002i−2i00002-22-200000000000002i−2i00000000
χ422-22-2-22-2222-2-2-22-22200002i−2i2i−2i-20000000000002i−2i0000-22-220000000000000−2i2i00000000
χ432-22-2-22-2222-2-2-22-2220000−2i2i−2i2i-2000000000000−2i2i00002-22-20000000000000−2i2i00000000
χ442-22-2-22-2222-2-2-22-2220000−2i2i−2i2i-2000000000000−2i2i0000-22-2200000000000002i−2i00000000
χ452-22-2-22-22-2222-22-2-2-22i−2i2i−2i2i−2i2i−2i2000000002i−2i00−2i2i00000000000000000002-20000000000
χ462-22-2-22-22-2222-22-2-2-22i−2i2i−2i−2i2i−2i2i2000000002i−2i002i−2i0000000000000000000-220000000000
χ472-22-2-22-22-2222-22-2-2-2−2i2i−2i2i2i−2i2i−2i200000000−2i2i00−2i2i0000000000000000000-220000000000
χ482-22-2-22-22-2222-22-2-2-2−2i2i−2i2i−2i2i−2i2i200000000−2i2i002i−2i00000000000000000002-20000000000
χ492-22-2-22-22-2-2222-22-222i−2i2i−2i0000-200000000−2i2i000000000000002i−2i2i−2i00000000002-200000
χ502-22-2-22-22-2-2222-22-222i−2i2i−2i0000-200000000−2i2i00000000000000−2i2i−2i2i0000000000-2200000
χ512-22-2-22-22-2-2222-22-22−2i2i−2i2i0000-2000000002i−2i000000000000002i−2i2i−2i0000000000-2200000
χ522-22-2-22-22-2-2222-22-22−2i2i−2i2i0000-2000000002i−2i00000000000000−2i2i−2i2i00000000002-200000
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
χ5844-44-4-4-440400-4-440000000000000002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ5944-44-4-4-440400-4-44000000000000000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ6044-4-4-444-440-44000-4000000000022−2222−22000000000000000000−2222000000000000000000000
χ6144-4-4-444-440-44000-40000000000−2222−222200000000000000000022−22000000000000000000000
χ624-44-4-44-444-4-4-44-444-4000000004000000000000000000000000000000000000000000000
χ634-4-4444-4-4404-4000-404-4-4400000000000000000000000000000000000000000000000000
χ644-4-4444-4-4404-4000-40-444-400000000000000000000000000000000000000000000000000
χ654-4-4444-4-4-40-44000400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ664-4-4444-4-4-40-4400040000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ674-4-4-44-44404004-4-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ684-4-4-44-44404004-4-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ694-4-4-44-4440-400-4440000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-44-4440-400-444000000-444-40000000000000000000000000000000000000000000000
χ718-888-8-88-8000000000000000000000000000000000000000000000000000000000000000

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