Finite Group Databasebeta

← Group #307990

Character table — Group #307990

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1111111111111-1-11-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-1
χ911111111111111111-1-1-1-11111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
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
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-111-1111-1-11111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111-1111111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-11
χ17222222222-2-22-222-2-222220000-22222000022-2-200000000-2-2000000000000-20000000000
χ18222222222-2-22-222-2-222220000-2-2-2-2-20000-2-2-2-2000000002200000000000020000000000
χ19222222222-2-22-222-2-2-2-2-2-20000-222220000-2-22200000000-2-200000000000020000000000
χ20222222222-2-22-222-2-2-2-2-2-20000-2-2-2-2-2000022220000000022000000000000-20000000000
χ2122222222-222-22-2-22-200002222-200002222000022-2-2000000-2-20000000000000-20000000
χ2222222222-222-22-2-22-200002222-20000-2-2-2-20000-2-2-2-200000022000000000000020000000
χ2322222222-222-22-2-22-20000-2-2-2-2-2000022220000-2-222000000-2-2000000000000020000000
χ2422222222-222-22-2-22-20000-2-2-2-2-20000-2-2-2-200002222000000220000000000000-20000000
χ252222-2-2-2-220020-2-20022-2-20000022-2-222−2−22-20000000000002−222−2−222−2−200000000002−20
χ262222-2-2-2-220020-2-20022-2-20000022-2-2−2−2222-2000000000000−22−2−222−2−2220000000000−220
χ272222-2-2-2-220020-2-20022-2-200000-2-22222−2−2-220000000000002−222−2−2−2−2220000000000−220
χ282222-2-2-2-220020-2-20022-2-200000-2-222−2−222-22000000000000−22−2−22222−2−200000000002−20
χ292222-2-2-2-220020-2-200-2-2220000022-2-222−2−2-220000000000002−2−2−22222−2−20000000000−220
χ302222-2-2-2-220020-2-200-2-2220000022-2-2−2−222-22000000000000−2222−2−2−2−22200000000002−20
χ312222-2-2-2-220020-2-200-2-22200000-2-22222−2−22-20000000000002−2−2−222−2−22200000000002−20
χ322222-2-2-2-220020-2-200-2-22200000-2-222−2−2222-2000000000000−2222−2−222−2−20000000000−220
χ3322-2-2-22-2202-20200-2000002i2i−2i−2i02−22−22-22-200002i−2i00i2i2−i2−i22−20000002−22−200000000i2−i2000
χ3422-2-2-22-2202-20200-2000002i2i−2i−2i02−22−2-22-220000−2i2i00i2i2−i2−i22−2000000−22−2200000000−i2i2000
χ3522-2-2-22-2202-20200-2000002i2i−2i−2i0−22−222-22-200002i−2i00−i2−i2i2i2−22000000−22−2200000000−i2i2000
χ3622-2-2-22-2202-20200-2000002i2i−2i−2i0−22−22-22-220000−2i2i00−i2−i2i2i2−220000002−22−200000000i2−i2000
χ3722-2-2-22-2202-20200-200000−2i−2i2i2i02−22−22-22-20000−2i2i00−i2−i2i2i22−20000002−22−200000000−i2i2000
χ3822-2-2-22-2202-20200-200000−2i−2i2i2i02−22−2-22-2200002i−2i00−i2−i2i2i22−2000000−22−2200000000i2−i2000
χ3922-2-2-22-2202-20200-200000−2i−2i2i2i0−22−222-22-20000−2i2i00i2i2−i2−i2−22000000−22−2200000000i2−i2000
χ4022-2-2-22-2202-20200-200000−2i−2i2i2i0−22−22-22-2200002i−2i00i2i2−i2−i2−220000002−22−200000000−i2i2000
χ412-2-2222-2-2222-2-22-2-222-22-20000-200000000002-200002-22-20000000000002-200000000000
χ422-2-2222-2-2222-2-22-2-222-22-20000-200000000002-20000-22-22000000000000-2200000000000
χ432-2-2222-2-2222-2-22-2-22-22-220000-20000000000-2200002-22-2000000000000-2200000000000
χ442-2-2222-2-2222-2-22-2-22-22-220000-20000000000-220000-22-220000000000002-200000000000
χ452-2-2222-2-22-2-2-222-22-22-22-22i−2i2i−2i20000000000-22002i−2i00000000000000000002i−2i00000000
χ462-2-2222-2-22-2-2-222-22-22-22-2−2i2i−2i2i20000000000-2200−2i2i0000000000000000000−2i2i00000000
χ472-2-2222-2-22-2-2-222-22-2-22-222i−2i2i−2i200000000002-2002i−2i0000000000000000000−2i2i00000000
χ482-2-2222-2-22-2-2-222-22-2-22-22−2i2i−2i2i200000000002-200−2i2i00000000000000000002i−2i00000000
χ492-2-2222-2-2-2-2-222-222200002i−2i2i−2i-200000000000000−2i2i000000002-22-200000000002i−2i00000
χ502-2-2222-2-2-2-2-222-222200002i−2i2i−2i-200000000000000−2i2i00000000-22-220000000000−2i2i00000
χ512-2-2222-2-2-2-2-222-22220000−2i2i−2i2i-2000000000000002i−2i000000002-22-20000000000−2i2i00000
χ522-2-2222-2-2-2-2-222-22220000−2i2i−2i2i-2000000000000002i−2i00000000-22-2200000000002i−2i00000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ544444-4-4-4-4-400-40440000000000000002222−22−2200000000000000−2222000000000000000000000
χ554444-4-4-4-4-400-4044000000000000000−22−2222220000000000000022−22000000000000000000000
χ5644-4-44-44-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ5744-4-44-44-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ5844-4-44-44-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ5944-4-44-44-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ6044-4-4-44-440-440-4004000000000022−2222−220000000000000000−222200000000000000000000000
χ6144-4-4-44-440-440-40040000000000−2222−2222000000000000000022−2200000000000000000000000
χ624-44-4-444-404-40-4004000000000000000000000000002i2−2i2−2i22i20000000000000000000000000
χ634-44-4-444-404-40-400400000000000000000000000000−2i22i22i2−2i20000000000000000000000000
χ644-44-4-444-40-440400-4000004-4-440000000000000000000000000000000000000000000000
χ654-44-4-444-40-440400-400000-444-40000000000000000000000000000000000000000000000
χ664-4-4444-4-4-4444-4-44-4-4000000004000000000000000000000000000000000000000000000
χ674-4-44-4-444400-40-44004-4-4400000000000000000000000000000000000000000000000000
χ684-4-44-4-444400-40-4400-444-400000000000000000000000000000000000000000000000000
χ694-4-44-4-444-400404-40000000000000000000000000000000000022−22−222200000000000000000
χ704-4-44-4-444-400404-400000000000000000000000000000000000−222222−2200000000000000000
χ718-88-88-8-88000000000000000000000000000000000000000000000000000000000000000

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