Finite Group Databasebeta

← Group #308116

Character table — Group #308116

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-11-1-111-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-11-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-11111-1-1111111-1-1-1-1-111-1-1-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111111-1-1-111-1-111-1
χ911111111111111111-1-1-1-1111111111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-111-1-111111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111111-1-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111-1-1111-1-1-1-1-1-11
χ17222222222-2-22-222-2-222220000-22222000000-2-222000000-2-2000000000000000-20000000
χ18222222222-2-22-222-2-222220000-2-2-2-2-2000000-2-2-2-20000002200000000000000020000000
χ19222222222-2-22-222-2-2-2-2-2-20000-2222200000022-2-2000000-2-200000000000000020000000
χ20222222222-2-22-222-2-2-2-2-2-20000-2-2-2-2-2000000222200000022000000000000000-20000000
χ2122222222-222-22-2-22-200002222-200002222-2-2000022000000-2-200000000-2000000000000
χ2222222222-222-22-2-22-200002222-20000-2-2-2-2-2-20000-2-200000022000000002000000000000
χ2322222222-222-22-2-22-20000-2-2-2-2-200002222220000-2-2000000-2-2000000002000000000000
χ2422222222-222-22-2-22-20000-2-2-2-2-20000-2-2-2-2220000220000002200000000-2000000000000
χ25222-2-2-2-22-200202-2002i2i−2i−2i0000022-2-2i2i2−i2−i200002i−2i00000000i2−i222−2−2i2i2−i2−i200000000002−20
χ26222-2-2-2-22-200202-2002i2i−2i−2i0000022-2-2−i2−i2i2i200002i−2i00000000−i2i2−2−222−i2−i2i2i20000000000−220
χ27222-2-2-2-22-200202-2002i2i−2i−2i00000-2-222i2i2−i2−i20000−2i2i00000000i2−i222−2−2−i2−i2i2i20000000000−220
χ28222-2-2-2-22-200202-2002i2i−2i−2i00000-2-222−i2−i2i2i20000−2i2i00000000−i2i2−2−222i2i2−i2−i200000000002−20
χ29222-2-2-2-22-200202-200−2i−2i2i2i0000022-2-2i2i2−i2−i20000−2i2i00000000i2−i2−2−222i2i2−i2−i20000000000−220
χ30222-2-2-2-22-200202-200−2i−2i2i2i0000022-2-2−i2−i2i2i20000−2i2i00000000−i2i222−2−2−i2−i2i2i200000000002−20
χ31222-2-2-2-22-200202-200−2i−2i2i2i00000-2-222i2i2−i2−i200002i−2i00000000i2−i2−2−222−i2−i2i2i200000000002−20
χ32222-2-2-2-22-200202-200−2i−2i2i2i00000-2-222−i2−i2i2i200002i−2i00000000−i2i222−2−2i2i2−i2−i20000000000−220
χ3322-2-2-222-202-20-2002000002i2i−2i−2i02−22−22i−2i2i−2i0000002-2i2i2−i2−i22−2000000i2−i2i2−i2000000002−2000
χ3422-2-2-222-202-20-2002000002i2i−2i−2i02−22−2−2i2i−2i2i000000-22i2i2−i2−i22−2000000−i2i2−i2i200000000−22000
χ3522-2-2-222-202-20-2002000002i2i−2i−2i0−22−222i−2i2i−2i0000002-2−i2−i2i2i2−22000000−i2i2−i2i200000000−22000
χ3622-2-2-222-202-20-2002000002i2i−2i−2i0−22−22−2i2i−2i2i000000-22−i2−i2i2i2−22000000i2−i2i2−i2000000002−2000
χ3722-2-2-222-202-20-200200000−2i−2i2i2i02−22−22i−2i2i−2i000000-22−i2−i2i2i22−2000000i2−i2i2−i200000000−22000
χ3822-2-2-222-202-20-200200000−2i−2i2i2i02−22−2−2i2i−2i2i0000002-2−i2−i2i2i22−2000000−i2i2−i2i2000000002−2000
χ3922-2-2-222-202-20-200200000−2i−2i2i2i0−22−222i−2i2i−2i000000-22i2i2−i2−i2−22000000−i2i2−i2i2000000002−2000
χ4022-2-2-222-202-20-200200000−2i−2i2i2i0−22−22−2i2i−2i2i0000002-2i2i2−i2−i2−22000000i2−i2i2−i200000000−22000
χ412-222-22-2-2222-2-22-2-222-22-20000-200000000002-200002-22-200000000000002-20000000000
χ422-222-22-2-2222-2-22-2-222-22-20000-200000000002-20000-22-220000000000000-220000000000
χ432-222-22-2-2222-2-22-2-22-22-220000-20000000000-2200002-22-20000000000000-220000000000
χ442-222-22-2-2222-2-22-2-22-22-220000-20000000000-220000-22-2200000000000002-20000000000
χ452-222-22-2-22-2-2-222-22-22-22-22i−2i2i−2i2000000002i−2i-22000000000000000000000002i−2i00000000
χ462-222-22-2-22-2-2-222-22-22-22-2−2i2i−2i2i200000000−2i2i-2200000000000000000000000−2i2i00000000
χ472-222-22-2-22-2-2-222-22-2-22-222i−2i2i−2i2000000002i−2i2-200000000000000000000000−2i2i00000000
χ482-222-22-2-22-2-2-222-22-2-22-22−2i2i−2i2i200000000−2i2i2-2000000000000000000000002i−2i00000000
χ492-222-22-2-2-2-2-222-222200002i−2i2i−2i-200000000−2i2i000000000000002-22-200000000002i−2i00000
χ502-222-22-2-2-2-2-222-222200002i−2i2i−2i-200000000−2i2i00000000000000-22-220000000000−2i2i00000
χ512-222-22-2-2-2-2-222-22220000−2i2i−2i2i-2000000002i−2i000000000000002-22-20000000000−2i2i00000
χ522-222-22-2-2-2-2-222-22220000−2i2i−2i2i-2000000002i−2i00000000000000-22-2200000000002i−2i00000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-4-44400-40-440000000000000002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ55444-4-4-4-44400-40-44000000000000000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ5644-444-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ5744-444-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ5844-444-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ5944-444-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ6044-4-4-444-40-440400-4000000000022−2222−220000000000000000−222200000000000000000000000
χ6144-4-4-444-40-440400-40000000000−2222−2222000000000000000022−2200000000000000000000000
χ624-444-44-4-4-4444-4-44-4-4000000004000000000000000000000000000000000000000000000
χ634-44-44-44-440040-4-40000000000000000000000000000000000022−22−222200000000000000000
χ644-44-44-44-440040-4-400000000000000000000000000000000000−222222−2200000000000000000
χ654-44-44-44-4-400-4044004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ664-44-44-44-4-400-404400−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ674-4-4-444-4404-40400-4000000000000000000000000002i2−2i2−2i22i20000000000000000000000000
χ684-4-4-444-4404-40400-400000000000000000000000000−2i22i22i2−2i20000000000000000000000000
χ694-4-4-444-440-440-4004000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-444-440-440-400400000-444-40000000000000000000000000000000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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