Finite Group Databasebeta

← Group #275397

Character table — Group #275397

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444224444444444444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-111111111-1-111-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ1011111111-1-1-1-111111111-1-111-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-11111-11
χ1211111111-1-1-1-111111111-1-111-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-111-1-11-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-11
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111111-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-111-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-1-11
χ172222222222222-2-222-2-22-2-2-2-222-222-2-222-2-2000000000000000000000000000000
χ182222222222222-2-222-2-22-2-2-2-222-2-2-222-2-222000000000000000000000000000000
χ19222222222222-222-2-222-222-2-2-2-2-20000000022220000-2-2-2-2000000000000000000
χ20222222222222-222-2-222-222-2-2-2-2-200000000-2-2-2-200002222000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-220000000000000000000000000000002i−2i2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-22000000000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-2-2-22-2-222-2-2222-2-2-2-2222-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2-22-2-222-2-2222-2-2-2-22-2-22222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-2-2-22220000000022-2-20000-2-222000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-2-2-222200000000-2-222000022-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000000000000000000000000000−2i2i2i−2i0000
χ292-222-22-2-20000-22-22-22-22002-200000002i−2i2i−2i00000000000022-2-22i−2i000000000000
χ302-222-22-2-20000-22-22-22-22002-200000002i−2i2i−2i000000000000-2-222−2i2i000000000000
χ312-222-22-2-20000-22-22-22-22002-20000000−2i2i−2i2i00000000000022-2-2−2i2i000000000000
χ322-222-22-2-20000-22-22-22-22002-20000000−2i2i−2i2i000000000000-2-2222i−2i000000000000
χ332-222-22-2-20000-2-222-2-22200-2200000002i−2i−2i2i000022-2-200000000002i−2i0000000000
χ342-222-22-2-20000-2-222-2-22200-2200000002i−2i−2i2i0000-2-2220000000000−2i2i0000000000
χ352-222-22-2-20000-2-222-2-22200-220000000−2i2i2i−2i000022-2-20000000000−2i2i0000000000
χ362-222-22-2-20000-2-222-2-22200-220000000−2i2i2i−2i0000-2-22200000000002i−2i0000000000
χ372-22-2-2-22222-2-202200-2-202-2000000000000000002−22−22i−2i2i−2i2−22−20000i2−i20000i2−i200
χ382-22-2-2-22222-2-202200-2-202-2000000000000000002−22−2−2i2i−2i2i2−22−20000−i2i20000−i2i200
χ392-22-2-2-22222-2-202200-2-202-200000000000000000−22−222i−2i2i−2i−22−220000−i2i20000−i2i200
χ402-22-2-2-22222-2-202200-2-202-200000000000000000−22−22−2i2i−2i2i−22−220000i2−i20000i2−i200
χ412-22-2-2-222-2-22202200-2-20-22000000000000000002−22−22i−2i−2i2i−22−220000i2−i20000−i2i200
χ422-22-2-2-222-2-22202200-2-20-22000000000000000002−22−2−2i2i2i−2i−22−220000−i2i20000i2−i200
χ432-22-2-2-222-2-22202200-2-20-2200000000000000000−22−222i−2i−2i2i2−22−20000−i2i20000i2−i200
χ442-22-2-2-222-2-22202200-2-20-2200000000000000000−22−22−2i2i2i−2i2−22−20000i2−i20000−i2i200
χ45444-44-4-4-4000004-400-44000000000000000000000000000022−22−222200000000000000
χ46444-44-4-4-4000004-400-440000000000000000000000000000−222222−2200000000000000
χ47444-44-4-4-400000-44004-40000000000000000000022−22−22220000000000000000000000
χ48444-44-4-4-400000-44004-400000000000000000000−222222−220000000000000000000000
χ4944-4-4-444-44i−4i4i−4i400-4-400400004i−4i000000000000000000000000000000000000000
χ5044-4-4-444-44i−4i4i−4i-4004400-40000−4i4i000000000000000000000000000000000000000
χ5144-4-4-444-4−4i4i−4i4i400-4-40040000−4i4i000000000000000000000000000000000000000
χ5244-4-4-444-4−4i4i−4i4i-4004400-400004i−4i000000000000000000000000000000000000000
χ534-444-44-4-4000044-4-444-4-400-4400000000000000000000000000000000000000000
χ544-444-44-4-400004-44-44-44-4004-400000000000000000000000000000000000000000
χ554-44-4-4-44444-4-40-4-400440-440000000000000000000000000000000000000000000
χ564-44-4-4-444-4-4440-4-4004404-40000000000000000000000000000000000000000000
χ574-4-444-44-44i−4i−4i4i0000000000000000000000022−222i2−2i200000000000000000000000000
χ584-4-444-44-44i−4i−4i4i00000000000000000000000−2222−2i22i200000000000000000000000000
χ594-4-444-44-4−4i4i4i−4i0000000000000000000000022−22−2i22i200000000000000000000000000
χ604-4-444-44-4−4i4i4i−4i00000000000000000000000−22222i2−2i200000000000000000000000000
χ614-4-4-444-4400004004-400-400000004i−4i000000000000000000000000000000000000
χ624-4-4-444-4400004004-400-40000000−4i4i000000000000000000000000000000000000
χ634-4-4-444-440000-400-440040000000004-40000000000000000000000000000000000
χ644-4-4-444-440000-400-44004000000000-440000000000000000000000000000000000
χ6588-88-8-8-88000000000000000000000000000000000000000000000000000000000

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