Finite Group Databasebeta

← Group #310451

Character table — Group #310451

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-11
χ51111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-111-1-111-1
χ911111111111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111
χ1011111111111111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-11111-11-1-1-1-1-1-11111-1-1-1
χ1111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-111-1-111-1-111-1-1-1-1-1-1111111111-11111-1-1-1-111-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-11111-1-11111-1
χ17222222222-22-2-222-2-22222-20000000022-2-2000022-2-200000000-200000000000000
χ18222222222-22-2-222-2-22222-200000000-2-2-2-20000-2-22200000000200000000000000
χ19222222222-22-2-222-2-2-2-2-2-2-20000000022220000-2-22200000000-200000000000000
χ20222222222-22-2-222-2-2-2-2-2-2-200000000-2-222000022-2-200000000200000000000000
χ2122222222-22-222-2-22-20000-2222222-2-20000-2-2-2-2000000000000020000000000000
χ2222222222-22-222-2-22-20000-22222-2-222000022-2-20000000000000-20000000000000
χ2322222222-22-222-2-22-20000-2-2-2-2-222220000-2-2220000000000000-20000000000000
χ2422222222-22-222-2-22-20000-2-2-2-2-2-2-2-2-200002222000000000000020000000000000
χ2522-2-2-222-220-200-22002i2i−2i−2i0i2i2−i2−i200002-20000i2−i22i−2i0022−2−222−2−2000000000000i2−i20
χ2622-2-2-222-220-200-22002i2i−2i−2i0i2i2−i2−i20000-220000i2−i2−2i2i0022−2−2−2−222000000000000−i2i20
χ2722-2-2-222-220-200-22002i2i−2i−2i0−i2−i2i2i200002-20000−i2i22i−2i00−2−222−2−222000000000000−i2i20
χ2822-2-2-222-220-200-22002i2i−2i−2i0−i2−i2i2i20000-220000−i2i2−2i2i00−2−22222−2−2000000000000i2−i20
χ2922-2-2-222-220-200-2200−2i−2i2i2i0i2i2−i2−i200002-20000i2−i2−2i2i00−2−222−2−222000000000000i2−i20
χ3022-2-2-222-220-200-2200−2i−2i2i2i0i2i2−i2−i20000-220000i2−i22i−2i00−2−22222−2−2000000000000−i2i20
χ3122-2-2-222-220-200-2200−2i−2i2i2i0−i2−i2i2i200002-20000−i2i2−2i2i0022−2−222−2−2000000000000−i2i20
χ3222-2-2-222-220-200-2200−2i−2i2i2i0−i2−i2i2i20000-220000−i2i22i−2i0022−2−2−2−222000000000000i2−i20
χ332-2-22-22-2222-2-2-22-2222i−2i2i−2i-200000000002i−2i000000000000000000002i−2i002-200000
χ342-2-22-22-2222-2-2-22-2222i−2i2i−2i-200000000002i−2i00000000000000000000−2i2i00-2200000
χ352-2-22-22-2222-2-2-22-222−2i2i−2i2i-20000000000−2i2i000000000000000000002i−2i00-2200000
χ362-2-22-22-2222-2-2-22-222−2i2i−2i2i-20000000000−2i2i00000000000000000000−2i2i002-200000
χ372-2-22-22-222-2-2222-2-2-22i−2i2i−2i200002i−2i0000−2i2i2i−2i000000000000000000002-20000000
χ382-2-22-22-222-2-2222-2-2-22i−2i2i−2i20000−2i2i0000−2i2i−2i2i00000000000000000000-220000000
χ392-2-22-22-222-2-2222-2-2-2−2i2i−2i2i200002i−2i00002i−2i2i−2i00000000000000000000-220000000
χ402-2-22-22-222-2-2222-2-2-2−2i2i−2i2i20000−2i2i00002i−2i−2i2i000000000000000000002-20000000
χ412-2-22-22-22-2-2222-22-220000-200002i−2i000000−2i2i0000002i−2i2i−2i0000002-200000000000
χ422-2-22-22-22-2-2222-22-220000-200002i−2i000000−2i2i000000−2i2i−2i2i000000-2200000000000
χ432-2-22-22-22-2-2222-22-220000-20000−2i2i0000002i−2i0000002i−2i2i−2i000000-2200000000000
χ442-2-22-22-22-2-2222-22-220000-20000−2i2i0000002i−2i000000−2i2i−2i2i0000002-200000000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-440404-400-400000000000000000000000000000022−2222−22000000000000000
χ47444-4-4-4-440404-400-4000000000000000000000000000000−2222−2222000000000000000
χ48444-4-4-4-440-40-440040000004i−4i4i−4i000000000000000000000000000000000000000
χ49444-4-4-4-440-40-44004000000−4i4i−4i4i000000000000000000000000000000000000000
χ5044-444-4-4-40000000000000022−22−22220000000000000022−2200002-2-22000000000000000
χ5144-444-4-4-40000000000000022−22−222200000000000000−22220000-222-2000000000000000
χ5244-444-4-4-400000000000000−222222−220000000000000022−220000-222-2000000000000000
χ5344-444-4-4-400000000000000−222222−2200000000000000−222200002-2-22000000000000000
χ5444-4-4-444-4-404004-400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ5544-4-4-444-4-404004-40000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ564-44-444-4-440400-4-4004-4-4400000000000000000000000000000000000000000000
χ574-44-444-4-440400-4-400-444-400000000000000000000000000000000000000000000
χ584-44-444-4-4-40-400440000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ594-44-444-4-4-40-40044000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ604-4-44-44-44-444-4-4-444-4000040000000000000000000000000000000000000000000
χ614-4-4-44-444040-4400-40000000000004i−4i00000000000000000000000000000000000
χ624-4-4-44-444040-4400-4000000000000−4i4i00000000000000000000000000000000000
χ634-4-4-44-4440-404-40040000000000000000000000000000000000000000000022−22000
χ644-4-4-44-4440-404-400400000000000000000000000000000000000000000000−2222000
χ658-888-8-88-8000000000000000000000000000000000000000000000000000000000

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