Finite Group Databasebeta

← Group #310504

Character table — Group #310504

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888222244448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-111-1-111-1
χ71111111111111111111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-111-1
χ81111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11
χ911111111111111111-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-1111111-1-11111-1-1-1-1111111-1-1-1-11-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-111-1-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-11-1-11-1-1-1-1111
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-1-11111-1-1-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-111-1111-1-111-1-1-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1111
χ17222222222-22-2-222-2-20000-22222002222-2-20000000000-2-200000000-20000000000
χ18222222222-22-2-222-2-20000-2222200-2-2-2-2220000000000-2-20000000020000000000
χ19222222222-22-2-222-2-20000-2-2-2-2-20022-2-22200000000002200000000-20000000000
χ20222222222-22-2-222-2-20000-2-2-2-2-200-2-222-2-20000000000220000000020000000000
χ2122222222-22-222-2-22-22222-20000-2-20000002222-2-200000000000000000-20000000
χ2222222222-22-222-2-22-22222-20000-2-2000000-2-2-2-2220000000000000000020000000
χ2322222222-22-222-2-22-2-2-2-2-2-200002200000022-2-22200000000000000000-20000000
χ2422222222-22-222-2-22-2-2-2-2-2-2000022000000-2-222-2-20000000000000000020000000
χ2522-2-2-2-2220202-200-202i2i−2i−2i022−2−2000000002i−2i2-200i2i2−i2−i22−222−2−200000000i2−i200000
χ2622-2-2-2-2220202-200-202i2i−2i−2i022−2−200000000−2i2i-2200i2i2−i2−i22−2−2−22200000000−i2i200000
χ2722-2-2-2-2220202-200-202i2i−2i−2i0−2−222000000002i−2i2-200−i2−i2i2i2−22−2−22200000000−i2i200000
χ2822-2-2-2-2220202-200-202i2i−2i−2i0−2−22200000000−2i2i-2200−i2−i2i2i2−2222−2−200000000i2−i200000
χ2922-2-2-2-2220202-200-20−2i−2i2i2i022−2−2000000002i−2i-2200−i2−i2i2i22−2−2−22200000000i2−i200000
χ3022-2-2-2-2220202-200-20−2i−2i2i2i022−2−200000000−2i2i2-200−i2−i2i2i22−222−2−200000000−i2i200000
χ3122-2-2-2-2220202-200-20−2i−2i2i2i0−2−222000000002i−2i-2200i2i2−i2−i2−2222−2−200000000−i2i200000
χ3222-2-2-2-2220202-200-20−2i−2i2i2i0−2−22200000000−2i2i2-200i2i2−i2−i2−22−2−22200000000i2−i200000
χ332-222-2-22-222-2-2-22-2220000-2000000002i−2i2i−2i0000002-22-2000000000002i−2i00000000
χ342-222-2-22-222-2-2-22-2220000-2000000002i−2i2i−2i000000-22-2200000000000−2i2i00000000
χ352-222-2-22-222-2-2-22-2220000-200000000−2i2i−2i2i0000002-22-200000000000−2i2i00000000
χ362-222-2-22-222-2-2-22-2220000-200000000−2i2i−2i2i000000-22-22000000000002i−2i00000000
χ372-222-2-22-22-2-2222-2-2-22i−2i2i−2i200002i−2i002i−2i−2i2i00000000000000002-20000000000000
χ382-222-2-22-22-2-2222-2-2-22i−2i2i−2i200002i−2i00−2i2i2i−2i0000000000000000-220000000000000
χ392-222-2-22-22-2-2222-2-2-2−2i2i−2i2i20000−2i2i002i−2i−2i2i0000000000000000-220000000000000
χ402-222-2-22-22-2-2222-2-2-2−2i2i−2i2i20000−2i2i00−2i2i2i−2i00000000000000002-20000000000000
χ412-222-2-22-2-2-2222-22-222i−2i2i−2i-20000−2i2i0000000000000000000000002-2000000002i−2i0
χ422-222-2-22-2-2-2222-22-222i−2i2i−2i-20000−2i2i000000000000000000000000-2200000000−2i2i0
χ432-222-2-22-2-2-2222-22-22−2i2i−2i2i-200002i−2i0000000000000000000000002-200000000−2i2i0
χ442-222-2-22-2-2-2222-22-22−2i2i−2i2i-200002i−2i000000000000000000000000-22000000002i−2i0
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-4000000000000002i2−2i22i2−2i200000000000022−220000002i−2i2i−2i000000000000000
χ47444-44-4-4-4000000000000002i2−2i22i2−2i2000000000000−2222000000−2i2i−2i2i000000000000000
χ48444-44-4-4-400000000000000−2i22i2−2i22i200000000000022−22000000−2i2i−2i2i000000000000000
χ49444-44-4-4-400000000000000−2i22i2−2i22i2000000000000−22220000002i−2i2i−2i000000000000000
χ5044-44-44-4-440-400-4400000004i−4i−4i4i000000000000000000000000000000000000000
χ5144-44-44-4-440-400-440000000−4i4i4i−4i000000000000000000000000000000000000000
χ5244-44-44-4-4-404004-400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ5344-44-44-4-4-404004-40000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ5444-4-4-4-4440-40-440040000002222−22−22000000000000000000−22220000000000000000000
χ5544-4-4-4-4440-40-44004000000−22−22222200000000000000000022−220000000000000000000
χ564-444-4-44-4-444-4-4-444-4000040000000000000000000000000000000000000000000
χ574-4-444-4-4440400-4-400000000000004i−4i00000000000000000000000000000000000
χ584-4-444-4-4440400-4-40000000000000−4i4i00000000000000000000000000000000000
χ594-4-444-4-44-40-4004400000000000000000000000000000000000000000000022−22000
χ604-4-444-4-44-40-40044000000000000000000000000000000000000000000000−2222000
χ614-4-4-4444-4040-4400-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ624-4-4-4444-4040-4400-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ634-4-4-4444-40-404-400404-4-4400000000000000000000000000000000000000000000
χ644-4-4-4444-40-404-40040-444-400000000000000000000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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