Finite Group Databasebeta

← Group #278408

Character table — Group #278408

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122222222222244444444444448888888888888888888888888816161616161632323232
order12222244444488884444444888888222444888888888888888888888888884488
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-11-1-11111111-111-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ611111111111111111-1-11-1-11111111-111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111-1-11-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111-1-11-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1
χ9111111111111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-111-1-11-11-1
χ10111111111111-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-11-11
χ11111111111111-1-1-1-11111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1111111-1-1-1-111111-111-1-1-11-11
χ12111111111111-1-1-1-11111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111-1-111-1-11111-11-1-1111-11-1
χ13111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-111-111-1-11111-1-1-1-111-1-1-1-111111-1-1-1111-1-11
χ14111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-111-1-11111-1111-1-1-111-1
χ15111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-11-1-1-111-111-1
χ16111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1111-1-11-1-11
χ172222222-222-220000-222-222-2000000-222-2-2-222000000000000-2-200000000000000
χ182222222-222-220000-222-222-2000000-2-2-2-222-2-20000000000002200000000000000
χ192222222-222-220000-2-2-2-2-2-2-20000002222-2-2-2-20000000000002200000000000000
χ202222222-222-220000-2-2-2-2-2-2-20000002-2-222222000000000000-2-200000000000000
χ21222222-22-2-22-22222-200200-2-2-2-2-22200000000000000000000000000002i−2i2i−2i0000
χ22222222-22-2-22-22222-200200-2-2-2-2-2220000000000000000000000000000−2i2i−2i2i0000
χ23222222-22-2-22-2-2-2-2-2-200200-22222-2-200000000000000000000000000002i−2i−2i2i0000
χ24222222-22-2-22-2-2-2-2-2-200200-22222-2-20000000000000000000000000000−2i2i2i−2i0000
χ252222-2-222-2-2222222-222-2-2-2222-2-2-2-2-2002000022-2-2000000000000000000000000
χ262222-2-222-2-2222222-2-2-2-222222-2-2-2-2200-20000-2-222000000000000000000000000
χ272222-2-222-2-222-2-2-2-2-222-2-2-22-2-22222-20020000-2-222000000000000000000000000
χ282222-2-222-2-222-2-2-2-2-2-2-2-2222-2-22222200-2000022-2-2000000000000000000000000
χ292222-2-22-2-2-2-2200002222-2-2-2000000200-2000000002i2i−2i−2i0000002i2i−2i−2i0000000000
χ302222-2-22-2-2-2-2200002222-2-2-2000000200-200000000−2i−2i2i2i000000−2i−2i2i2i0000000000
χ312222-2-22-2-2-2-2200002-2-2222-2000000-2002000000002i2i−2i−2i000000−2i−2i2i2i0000000000
χ322222-2-22-2-2-2-2200002-2-2222-2000000-200200000000−2i−2i2i2i0000002i2i−2i−2i0000000000
χ332222-2-2-22222-22222200-200-2-2-222-2-200000000000000002222000000-2-200000000
χ342222-2-2-22222-22222200-200-2-2-222-2-20000000000000000-2-2-2-20000002200000000
χ352222-2-2-22222-2-2-2-2-2200-200-222-2-222000000000000000022-2-2000000-2200000000
χ362222-2-2-22222-2-2-2-2-2200-200-222-2-2220000000000000000-2-2220000002-200000000
χ3722-2-22-2-202-20222−2−202i−2i02i−2i02−22−22−200002i−2i00i2−i2i2−i2i2−i2i2−i200002-22−22−20000000000
χ3822-2-22-2-202-20222−2−202i−2i02i−2i02−22−22−20000−2i2i00i2−i2i2−i2−i2i2−i2i20000-22−22−220000000000
χ3922-2-22-2-202-20222−2−20−2i2i0−2i2i02−22−22−200002i−2i00−i2i2−i2i2i2−i2i2−i20000-22−22−220000000000
χ4022-2-22-2-202-20222−2−20−2i2i0−2i2i02−22−22−20000−2i2i00−i2i2−i2i2−i2i2−i2i200002-22−22−20000000000
χ4122-2-22-2-202-202−2−22202i−2i02i−2i0−22−22−2200002i−2i00−i2i2−i2i2−i2i2−i2i200002-2−22−220000000000
χ4222-2-22-2-202-202−2−22202i−2i02i−2i0−22−22−220000−2i2i00−i2i2−i2i2i2−i2i2−i20000-222−22−20000000000
χ4322-2-22-2-202-202−2−2220−2i2i0−2i2i0−22−22−2200002i−2i00i2−i2i2−i2−i2i2−i2i20000-222−22−20000000000
χ4422-2-22-2-202-202−2−2220−2i2i0−2i2i0−22−22−220000−2i2i00i2−i2i2−i2i2−i2i2−i200002-2−22−220000000000
χ4522-2-2-22-20-220222−2−202i−2i0−2i2i02−2−22−2202-20002i−2ii2−i2−i2i22−2−22000000−i2i2i2−i20000000000
χ4622-2-2-22-20-220222−2−202i−2i0−2i2i02−2−22−220-22000−2i2ii2−i2−i2i2−222−2000000i2−i2−i2i20000000000
χ4722-2-2-22-20-220222−2−20−2i2i02i−2i02−2−22−2202-2000−2i2i−i2i2i2−i22−2−22000000i2−i2−i2i20000000000
χ4822-2-2-22-20-220222−2−20−2i2i02i−2i02−2−22−220-220002i−2i−i2i2i2−i2−222−2000000−i2i2i2−i20000000000
χ4922-2-2-22-20-2202−2−22202i−2i0−2i2i0−222−22−202-20002i−2i−i2i2i2−i2−222−2000000i2−i2−i2i20000000000
χ5022-2-2-22-20-2202−2−22202i−2i0−2i2i0−222−22−20-22000−2i2i−i2i2i2−i22−2−22000000−i2i2i2−i20000000000
χ5122-2-2-22-20-2202−2−2220−2i2i02i−2i0−222−22−202-2000−2i2ii2−i2−i2i2−222−2000000−i2i2i2−i20000000000
χ5222-2-2-22-20-2202−2−2220−2i2i02i−2i0−222−22−20-220002i−2ii2−i2−i2i22−2−22000000i2−i2−i2i20000000000
χ53444444-4-4-4-4-4-40000400-4004000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-40000-4004004000000000000000000000000000000000000000000
χ5544-4-44-440-440-42222−22−220000000−2222−222222−22000000000000000000000000000000000000
χ5644-4-44-440-440-4−22−222222000000022−2222−22−2222000000000000000000000000000000000000
χ5744-4-4-44404-40-42222−22−220000000−222222−22−2222000000000000000000000000000000000000
χ5844-4-4-44404-40-4−22−222222000000022−22−222222−22000000000000000000000000000000000000
χ594-4-44000400-404i−4i4i−4i000000000000000000000000000002i2−2i222−220000000000000000
χ604-4-44000400-404i−4i4i−4i00000000000000000000000000000−2i22i2−22220000000000000000
χ614-4-44000400-40−4i4i−4i4i000000000000000000000000000002i2−2i2−22220000000000000000
χ624-4-44000400-40−4i4i−4i4i00000000000000000000000000000−2i22i222−220000000000000000
χ638-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000
χ648-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000
χ658-8-88000-8008000000000000000000000000000000000000000000000000000000

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