Finite Group Databasebeta

← Group #7623024

Character table — Group #7623024

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222222224444444488888888888888881616161611112222222222222244444444888888888888888816161616
order124422244488888888444488882244888816161616161616164444224422244488888888444488882244888816161616161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ911-1-1-1-11-111-1-111-1-11111-1-11-11-11-11-111-1-111-1-111-1-11-11-111-1-1-1-11-111-1-111-1-11111-1-11-11-11-11-111-1-111-1-111-1-11-11-1
χ1011-1-1-1-11-111-1-111-1-11111-1-11-11-11-11-111-1-1-1-111-1-111-11-1111-1-1-1-11-111-1-111-1-11111-1-11-11-11-11-111-1-1-1-111-1-111-11-11
χ1111-1-1-1-11-111-1-111-1-11111-1-11-11-1-11-11-1-11111-1-111-1-1-11-1111-1-1-1-11-111-1-111-1-11111-1-11-11-1-11-11-1-11111-1-111-1-1-11-11
χ1211-1-1-1-11-111-1-111-1-11111-1-11-11-1-11-11-1-111-1-111-1-1111-11-111-1-1-1-11-111-1-111-1-11111-1-11-11-1-11-11-1-111-1-111-1-1111-11-1
χ1311-1-1-1-11-111-1-1-1-11111-1-1111-1-111-11-1-1-11111-1-1-1-1111-1-1111-1-1-1-11-111-1-1-1-11111-1-1111-1-111-11-1-1-11111-1-1-1-1111-1-11
χ1411-1-1-1-11-111-1-1-1-11111-1-1111-1-111-11-1-1-111-1-11111-1-1-111-111-1-1-1-11-111-1-1-1-11111-1-1111-1-111-11-1-1-111-1-11111-1-1-111-1
χ1511-1-1-1-11-111-1-1-1-11111-1-1111-1-11-11-1111-1-111-1-1-1-111-111-111-1-1-1-11-111-1-1-1-11111-1-1111-1-11-11-1111-1-111-1-1-1-111-111-1
χ1611-1-1-1-11-111-1-1-1-11111-1-1111-1-11-11-1111-1-1-1-11111-1-11-1-1111-1-1-1-11-111-1-1-1-11111-1-1111-1-11-11-1111-1-1-1-11111-1-11-1-11
χ172222222222-2-22222-2-2-2-2-2-2-2-222000000000000000000002222222222-2-22222-2-2-2-2-2-2-2-22200000000000000000000
χ182222222222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000000000002222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000
χ1922222-2-2-22-2220000220000-2-20000002i−2i2i−2i00000000000022222-2-2-22-2220000220000-2-20000002i−2i2i−2i000000000000
χ2022222-2-2-22-2220000220000-2-2000000−2i2i−2i2i00000000000022222-2-2-22-2220000220000-2-2000000−2i2i−2i2i000000000000
χ2122222-2-2-22-2-2-20000-2-2000022002-2-22000000000000000022222-2-2-22-2-2-20000-2-2000022002-2-220000000000000000
χ2222222-2-2-22-2-2-20000-2-200002200-222-2000000000000000022222-2-2-22-2-2-20000-2-200002200-222-20000000000000000
χ232222-22-2-2-2200222200000000-2-200000000i2−i2i2−i2i2−i2i2−i200002222-22-2-2-2200222200000000-2-200000000i2−i2i2−i2i2−i2i2−i20000
χ242222-22-2-2-2200222200000000-2-200000000−i2i2−i2i2−i2i2−i2i200002222-22-2-2-2200222200000000-2-200000000−i2i2−i2i2−i2i2−i2i20000
χ252222-22-2-2-2200-2-2-2-2000000002200000000i2−i2i2−i2−i2i2−i2i200002222-22-2-2-2200-2-2-2-2000000002200000000i2−i2i2−i2−i2i2−i2i20000
χ262222-22-2-2-2200-2-2-2-2000000002200000000−i2i2−i2i2i2−i2i2−i200002222-22-2-2-2200-2-2-2-2000000002200000000−i2i2−i2i2i2−i2i2−i20000
χ2722-2-22-2-22-220022-2-200000000-2200000000i2−i2−i2i2i2−i2−i2i2000022-2-22-2-22-220022-2-200000000-2200000000i2−i2−i2i2i2−i2−i2i20000
χ2822-2-22-2-22-220022-2-200000000-2200000000−i2i2i2−i2−i2i2i2−i2000022-2-22-2-22-220022-2-200000000-2200000000−i2i2i2−i2−i2i2i2−i20000
χ2922-2-22-2-22-2200-2-222000000002-200000000i2−i2−i2i2−i2i2i2−i2000022-2-22-2-22-2200-2-222000000002-200000000i2−i2−i2i2−i2i2i2−i20000
χ3022-2-22-2-22-2200-2-222000000002-200000000−i2i2i2−i2i2−i2−i2i2000022-2-22-2-22-2200-2-222000000002-200000000−i2i2i2−i2i2−i2−i2i20000
χ3122-2-2-22-222-2220000-2-200002-20022-2-2000000000000000022-2-2-22-222-2220000-2-200002-20022-2-20000000000000000
χ3222-2-2-22-222-2220000-2-200002-200-2-222000000000000000022-2-2-22-222-2220000-2-200002-200-2-2220000000000000000
χ3322-2-2-22-222-2-2-20000220000-220000002i−2i−2i2i00000000000022-2-2-22-222-2-2-20000220000-220000002i−2i−2i2i000000000000
χ3422-2-2-22-222-2-2-20000220000-22000000−2i2i2i−2i00000000000022-2-2-22-222-2-2-20000220000-22000000−2i2i2i−2i000000000000
χ3522-2-2-2-22-2222222-2-2-2-2-2-222-222-20000000000000000000022-2-2-2-22-2222222-2-2-2-2-2-222-222-200000000000000000000
χ3622-2-2-2-22-22222-2-222-2-222-2-2-22-220000000000000000000022-2-2-2-22-22222-2-222-2-222-2-2-22-2200000000000000000000
χ374444-4-444-4-40000000000000000000000000000000000004444-4-444-4-4000000000000000000000000000000000000
χ3844-4-4444-4-4-400000000000000000000000000000000000044-4-4444-4-4-4000000000000000000000000000000000000
χ394-44i−4i00000022−222i2−2i222−222i2−2i22-22i−2i0000000000000000000000004-44i−4i00000022−222i2−2i222−222i2−2i22-22i−2i000000000000000000000000
χ404-44i−4i00000022−22−2i22i2−22222i2−2i2-22−2i2i0000000000000000000000004-44i−4i00000022−22−2i22i2−22222i2−2i2-22−2i2i000000000000000000000000
χ414-44i−4i000000−22222i2−2i222−22−2i22i2-22−2i2i0000000000000000000000004-44i−4i000000−22222i2−2i222−22−2i22i2-22−2i2i000000000000000000000000
χ424-44i−4i000000−2222−2i22i2−2222−2i22i22-22i−2i0000000000000000000000004-44i−4i000000−2222−2i22i2−2222−2i22i22-22i−2i000000000000000000000000
χ434-4−4i4i00000022−222i2−2i2−2222−2i22i2-222i−2i0000000000000000000000004-4−4i4i00000022−222i2−2i2−2222−2i22i2-222i−2i000000000000000000000000
χ444-4−4i4i00000022−22−2i22i222−22−2i22i22-2−2i2i0000000000000000000000004-4−4i4i00000022−22−2i22i222−22−2i22i22-2−2i2i000000000000000000000000
χ454-4−4i4i000000−22222i2−2i2−22222i2−2i22-2−2i2i0000000000000000000000004-4−4i4i000000−22222i2−2i2−22222i2−2i22-2−2i2i000000000000000000000000
χ464-4−4i4i000000−2222−2i22i222−222i2−2i2-222i−2i0000000000000000000000004-4−4i4i000000−2222−2i22i222−222i2−2i2-222i−2i000000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ481111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ4911111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5011111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ51111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-111
χ52111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-1
χ53111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ54111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ5511-1-1-1-11-111-1-111-1-11111-1-11-11-11-11-111-1-111-1-111-1-11-11-1-1-11111-11-1-111-1-111-1-1-1-111-11-11-11-11-1-111-1-111-1-111-11-11
χ5611-1-1-1-11-111-1-111-1-11111-1-11-11-11-11-111-1-1-1-111-1-111-11-11-1-11111-11-1-111-1-111-1-1-1-111-11-11-11-11-1-11111-1-111-1-11-11-1
χ5711-1-1-1-11-111-1-111-1-11111-1-11-11-1-11-11-1-11111-1-111-1-1-11-11-1-11111-11-1-111-1-111-1-1-1-111-11-111-11-111-1-1-1-111-1-1111-11-1
χ5811-1-1-1-11-111-1-111-1-11111-1-11-11-1-11-11-1-111-1-111-1-1111-11-1-1-11111-11-1-111-1-111-1-1-1-111-11-111-11-111-1-111-1-111-1-1-11-11
χ5911-1-1-1-11-111-1-1-1-11111-1-1111-1-111-11-1-1-11111-1-1-1-1111-1-11-1-11111-11-1-11111-1-1-1-111-1-1-111-1-11-1111-1-1-1-11111-1-1-111-1
χ6011-1-1-1-11-111-1-1-1-11111-1-1111-1-111-11-1-1-111-1-11111-1-1-111-1-1-11111-11-1-11111-1-1-1-111-1-1-111-1-11-1111-1-111-1-1-1-1111-1-11
χ6111-1-1-1-11-111-1-1-1-11111-1-1111-1-11-11-1111-1-111-1-1-1-111-111-1-1-11111-11-1-11111-1-1-1-111-1-1-111-11-11-1-1-111-1-11111-1-11-1-11
χ6211-1-1-1-11-111-1-1-1-11111-1-1111-1-11-11-1111-1-1-1-11111-1-11-1-11-1-11111-11-1-11111-1-1-1-111-1-1-111-11-11-1-1-11111-1-1-1-111-111-1
χ632222222222-2-22222-2-2-2-2-2-2-2-22200000000000000000000-2-2-2-2-2-2-2-2-2-222-2-2-2-222222222-2-200000000000000000000
χ642222222222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2222200000000000000000000
χ6522222-2-2-22-2220000220000-2-20000002i−2i2i−2i000000000000-2-2-2-2-2222-22-2-20000-2-2000022000000−2i2i−2i2i000000000000
χ6622222-2-2-22-2220000220000-2-2000000−2i2i−2i2i000000000000-2-2-2-2-2222-22-2-20000-2-20000220000002i−2i2i−2i000000000000
χ6722222-2-2-22-2-2-20000-2-2000022002-2-220000000000000000-2-2-2-2-2222-22220000220000-2-200-222-20000000000000000
χ6822222-2-2-22-2-2-20000-2-200002200-222-20000000000000000-2-2-2-2-2222-22220000220000-2-2002-2-220000000000000000
χ692222-22-2-2-2200222200000000-2-200000000i2−i2i2−i2i2−i2i2−i20000-2-2-2-22-2222-200-2-2-2-2000000002200000000−i2i2−i2i2−i2i2−i2i20000
χ702222-22-2-2-2200222200000000-2-200000000−i2i2−i2i2−i2i2−i2i20000-2-2-2-22-2222-200-2-2-2-2000000002200000000i2−i2i2−i2i2−i2i2−i20000
χ712222-22-2-2-2200-2-2-2-2000000002200000000i2−i2i2−i2−i2i2−i2i20000-2-2-2-22-2222-200222200000000-2-200000000−i2i2−i2i2i2−i2i2−i20000
χ722222-22-2-2-2200-2-2-2-2000000002200000000−i2i2−i2i2i2−i2i2−i20000-2-2-2-22-2222-200222200000000-2-200000000i2−i2i2−i2−i2i2−i2i20000
χ7322-2-22-2-22-220022-2-200000000-2200000000i2−i2−i2i2i2−i2−i2i20000-2-222-222-22-200-2-222000000002-200000000−i2i2i2−i2−i2i2i2−i20000
χ7422-2-22-2-22-220022-2-200000000-2200000000−i2i2i2−i2−i2i2i2−i20000-2-222-222-22-200-2-222000000002-200000000i2−i2−i2i2i2−i2−i2i20000
χ7522-2-22-2-22-2200-2-222000000002-200000000i2−i2−i2i2−i2i2i2−i20000-2-222-222-22-20022-2-200000000-2200000000−i2i2i2−i2i2−i2−i2i20000
χ7622-2-22-2-22-2200-2-222000000002-200000000−i2i2i2−i2i2−i2−i2i20000-2-222-222-22-20022-2-200000000-2200000000i2−i2−i2i2−i2i2i2−i20000
χ7722-2-2-22-222-2220000-2-200002-20022-2-20000000000000000-2-2222-22-2-22-2-20000220000-2200-2-2220000000000000000
χ7822-2-2-22-222-2220000-2-200002-200-2-2220000000000000000-2-2222-22-2-22-2-20000220000-220022-2-20000000000000000
χ7922-2-2-22-222-2-2-20000220000-220000002i−2i−2i2i000000000000-2-2222-22-2-22220000-2-200002-2000000−2i2i2i−2i000000000000
χ8022-2-2-22-222-2-2-20000220000-22000000−2i2i2i−2i000000000000-2-2222-22-2-22220000-2-200002-20000002i−2i−2i2i000000000000
χ8122-2-2-2-22-2222222-2-2-2-2-2-222-222-200000000000000000000-2-22222-22-2-2-2-2-2-2222222-2-22-2-2200000000000000000000
χ8222-2-2-2-22-22222-2-222-2-222-2-2-22-2200000000000000000000-2-22222-22-2-2-2-222-2-222-2-2222-22-200000000000000000000
χ834444-4-444-4-4000000000000000000000000000000000000-4-4-4-444-4-444000000000000000000000000000000000000
χ8444-4-4444-4-4-4000000000000000000000000000000000000-4-444-4-4-4444000000000000000000000000000000000000
χ854-44i−4i00000022−222i2−2i222−222i2−2i22-22i−2i000000000000000000000000-44−4i4i000000−2222−2i22i2−2222−2i22i2-22−2i2i000000000000000000000000
χ864-44i−4i00000022−22−2i22i2−22222i2−2i2-22−2i2i000000000000000000000000-44−4i4i000000−22222i2−2i222−22−2i22i22-22i−2i000000000000000000000000
χ874-44i−4i000000−22222i2−2i222−22−2i22i2-22−2i2i000000000000000000000000-44−4i4i00000022−22−2i22i2−22222i2−2i22-22i−2i000000000000000000000000
χ884-44i−4i000000−2222−2i22i2−2222−2i22i22-22i−2i000000000000000000000000-44−4i4i00000022−222i2−2i222−222i2−2i2-22−2i2i000000000000000000000000
χ894-4−4i4i00000022−222i2−2i2−2222−2i22i2-222i−2i000000000000000000000000-444i−4i000000−2222−2i22i222−222i2−2i22-2−2i2i000000000000000000000000
χ904-4−4i4i00000022−22−2i22i222−22−2i22i22-2−2i2i000000000000000000000000-444i−4i000000−22222i2−2i2−22222i2−2i2-222i−2i000000000000000000000000
χ914-4−4i4i000000−22222i2−2i2−22222i2−2i22-2−2i2i000000000000000000000000-444i−4i00000022−22−2i22i222−22−2i22i2-222i−2i000000000000000000000000
χ924-4−4i4i000000−2222−2i22i222−222i2−2i2-222i−2i000000000000000000000000-444i−4i00000022−222i2−2i2−2222−2i22i22-2−2i2i000000000000000000000000

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