Finite Group Databasebeta

← Group #195113

Character table — Group #195113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222244444444888888888888888888888888881111111122224444444488888888888888888888888888
order12222222222244444444222244444444444444888888882222222222224444444422224444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111
χ7111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111
χ8111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1
χ911-11-1-11-111-1-1ii−i−i1-11-111-1-11-1i−ii−i1-1i−iii−i−i11-1-1ii−i−i11-11-1-11-111-1-1ii−i−i1-11-111-1-11-1i−ii−i1-1i−iii−i−i11-1-1ii−i−i
χ1011-11-1-11-111-1-1ii−i−i1-11-111-1-1-11−iii−i-11−iiii−i−i-1-111−i−iii11-11-1-11-111-1-1ii−i−i1-11-111-1-1-11−iii−i-11−iiii−i−i-1-111−i−iii
χ1111-11-1-11-111-1-1ii−i−i1-11-1-1-1111-1i−ii−i1-1i−i−i−iii-1-111−i−iii11-11-1-11-111-1-1ii−i−i1-11-1-1-1111-1i−ii−i1-1i−i−i−iii-1-111−i−iii
χ1211-11-1-11-111-1-1ii−i−i1-11-1-1-111-11−iii−i-11−ii−i−iii11-1-1ii−i−i11-11-1-11-111-1-1ii−i−i1-11-1-1-111-11−iii−i-11−ii−i−iii11-1-1ii−i−i
χ1311-11-1-11-111-1-1−i−iii1-11-111-1-11-1−ii−ii1-1−ii−i−iii11-1-1−i−iii11-11-1-11-111-1-1−i−iii1-11-111-1-11-1−ii−ii1-1−ii−i−iii11-1-1−i−iii
χ1411-11-1-11-111-1-1−i−iii1-11-111-1-1-11i−i−ii-11i−i−i−iii-1-111ii−i−i11-11-1-11-111-1-1−i−iii1-11-111-1-1-11i−i−ii-11i−i−i−iii-1-111ii−i−i
χ1511-11-1-11-111-1-1−i−iii1-11-1-1-1111-1−ii−ii1-1−iiii−i−i-1-111ii−i−i11-11-1-11-111-1-1−i−iii1-11-1-1-1111-1−ii−ii1-1−iiii−i−i-1-111ii−i−i
χ1611-11-1-11-111-1-1−i−iii1-11-1-1-111-11i−i−ii-11i−iii−i−i11-1-1−i−iii11-11-1-11-111-1-1−i−iii1-11-1-1-111-11i−i−ii-11i−iii−i−i11-1-1−i−iii
χ172222222222222222-2-2-2-200000000-2-200000000000000002222222222222222-2-2-2-200000000-2-20000000000000000
χ18222222222222-2-2-2-2-2-2-2-200000000220000000000000000222222222222-2-2-2-2-2-2-2-200000000220000000000000000
χ1922222222-2-2-2-200002-2-22000000220000-2-200000000000022222222-2-2-2-200002-2-22000000220000-2-2000000000000
χ2022222222-2-2-2-200002-2-22000000-2-200002200000000000022222222-2-2-2-200002-2-22000000-2-2000022000000000000
χ2122222222-2-2-2-20000-222-20000220000-2-20000000000000022222222-2-2-2-20000-222-20000220000-2-200000000000000
χ2222222222-2-2-2-20000-222-20000-2-20000220000000000000022222222-2-2-2-20000-222-20000-2-200002200000000000000
χ23222-22-2-2-22-2-222-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i2222-22-2-2-22-2-222-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ24222-22-2-2-22-2-222-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i2222-22-2-2-22-2-222-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ25222-22-2-2-22-2-22-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i2222-22-2-2-22-2-22-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ26222-22-2-2-22-2-22-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i2222-22-2-2-22-2-22-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ2722-22-2-22-222-2-22i2i−2i−2i-22-2200000000−2i2i000000000000000022-22-2-22-222-2-22i2i−2i−2i-22-2200000000−2i2i0000000000000000
χ2822-22-2-22-222-2-2−2i−2i2i2i-22-22000000002i−2i000000000000000022-22-2-22-222-2-2−2i−2i2i2i-22-22000000002i−2i0000000000000000
χ2922-22-2-22-2-2-222000022-2-20000002i−2i0000−2i2i00000000000022-22-2-22-2-2-222000022-2-20000002i−2i0000−2i2i000000000000
χ3022-22-2-22-2-2-222000022-2-2000000−2i2i00002i−2i00000000000022-22-2-22-2-2-222000022-2-2000000−2i2i00002i−2i000000000000
χ3122-22-2-22-2-2-2220000-2-22200002-20000-220000000000000022-22-2-22-2-2-2220000-2-22200002-20000-2200000000000000
χ3222-22-2-22-2-2-2220000-2-2220000-2200002-20000000000000022-22-2-22-2-2-2220000-2-2220000-2200002-200000000000000
χ3322-2-2-22-222-22-22i−2i−2i2i0000000000000000000000i2−i2−i2i2−222−222-2-2-22-222-22-22i−2i−2i2i0000000000000000000000i2−i2−i2i2−222−2
χ3422-2-2-22-222-22-22i−2i−2i2i0000000000000000000000−i2i2i2−i22−2−2222-2-2-22-222-22-22i−2i−2i2i0000000000000000000000−i2i2i2−i22−2−22
χ3522-2-2-22-222-22-2−2i2i2i−2i0000000000000000000000i2−i2−i2i22−2−2222-2-2-22-222-22-2−2i2i2i−2i0000000000000000000000i2−i2−i2i22−2−22
χ3622-2-2-22-222-22-2−2i2i2i−2i0000000000000000000000−i2i2i2−i2−222−222-2-2-22-222-22-2−2i2i2i−2i0000000000000000000000−i2i2i2−i2−222−2
χ37444-44-4-4-4-444-40000000000000000000000000000000000444-44-4-4-4-444-40000000000000000000000000000000000
χ3844-4-4-44-44-44-44000000000000000000000000000000000044-4-4-44-44-44-440000000000000000000000000000000000
χ394-444-44-4-4000000000000000000000000002i−2i2i−2i000000004-444-44-4-4000000000000000000000000002i−2i2i−2i00000000
χ404-444-44-4-400000000000000000000000000−2i2i−2i2i000000004-444-44-4-400000000000000000000000000−2i2i−2i2i00000000
χ414-44-4-4-4440000000000002-22-200000000000000000000004-44-4-4-4440000000000002-22-20000000000000000000000
χ424-44-4-4-444000000000000-22-2200000000000000000000004-44-4-4-444000000000000-22-220000000000000000000000
χ434-4-444-4-44000000000000000000000000002-2-22000000004-4-444-4-44000000000000000000000000002-2-2200000000
χ444-4-444-4-4400000000000000000000000000-222-2000000004-4-444-4-4400000000000000000000000000-222-200000000
χ454-4-4-4444-40000000000002-2-2200000000000000000000004-4-4-4444-40000000000002-2-220000000000000000000000
χ464-4-4-4444-4000000000000-222-200000000000000000000004-4-4-4444-4000000000000-222-20000000000000000000000
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
χ48111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111
χ4911111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111
χ5011111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1
χ51111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111
χ52111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-1
χ53111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-1-1-1
χ54111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111
χ5511-11-1-11-111-1-1ii−i−i1-11-111-1-11-1i−ii−i1-1i−iii−i−i11-1-1ii−i−i-1-11-111-11-1-111−i−iii-11-11-1-111-11−ii−ii-11−ii−i−iii-1-111−i−iii
χ5611-11-1-11-111-1-1ii−i−i1-11-111-1-1-11−iii−i-11−iiii−i−i-1-111−i−iii-1-11-111-11-1-111−i−iii-11-11-1-1111-1i−i−ii1-1i−i−i−iii11-1-1ii−i−i
χ5711-11-1-11-111-1-1ii−i−i1-11-1-1-1111-1i−ii−i1-1i−i−i−iii-1-111−i−iii-1-11-111-11-1-111−i−iii-11-1111-1-1-11−ii−ii-11−iiii−i−i11-1-1ii−i−i
χ5811-11-1-11-111-1-1ii−i−i1-11-1-1-111-11−iii−i-11−ii−i−iii11-1-1ii−i−i-1-11-111-11-1-111−i−iii-11-1111-1-11-1i−i−ii1-1i−iii−i−i-1-111−i−iii
χ5911-11-1-11-111-1-1−i−iii1-11-111-1-11-1−ii−ii1-1−ii−i−iii11-1-1−i−iii-1-11-111-11-1-111ii−i−i-11-11-1-111-11i−ii−i-11i−iii−i−i-1-111ii−i−i
χ6011-11-1-11-111-1-1−i−iii1-11-111-1-1-11i−i−ii-11i−i−i−iii-1-111ii−i−i-1-11-111-11-1-111ii−i−i-11-11-1-1111-1−iii−i1-1−iiii−i−i11-1-1−i−iii
χ6111-11-1-11-111-1-1−i−iii1-11-1-1-1111-1−ii−ii1-1−iiii−i−i-1-111ii−i−i-1-11-111-11-1-111ii−i−i-11-1111-1-1-11i−ii−i-11i−i−i−iii11-1-1−i−iii
χ6211-11-1-11-111-1-1−i−iii1-11-1-1-111-11i−i−ii-11i−iii−i−i11-1-1−i−iii-1-11-111-11-1-111ii−i−i-11-1111-1-11-1−iii−i1-1−ii−i−iii-1-111ii−i−i
χ632222222222222222-2-2-2-200000000-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000220000000000000000
χ64222222222222-2-2-2-2-2-2-2-200000000220000000000000000-2-2-2-2-2-2-2-2-2-2-2-22222222200000000-2-20000000000000000
χ6522222222-2-2-2-200002-2-22000000220000-2-2000000000000-2-2-2-2-2-2-2-222220000-222-2000000-2-2000022000000000000
χ6622222222-2-2-2-200002-2-22000000-2-2000022000000000000-2-2-2-2-2-2-2-222220000-222-2000000220000-2-2000000000000
χ6722222222-2-2-2-20000-222-20000220000-2-200000000000000-2-2-2-2-2-2-2-2222200002-2-220000-2-200002200000000000000
χ6822222222-2-2-2-20000-222-20000-2-200002200000000000000-2-2-2-2-2-2-2-2222200002-2-220000220000-2-200000000000000
χ69222-22-2-2-22-2-222-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i2-2-2-22-2222-222-2-22-220000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ70222-22-2-2-22-2-222-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i2-2-2-22-2222-222-2-22-220000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ71222-22-2-2-22-2-22-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i2-2-2-22-2222-222-22-22-20000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ72222-22-2-2-22-2-22-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i2-2-2-22-2222-222-22-22-20000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ7322-22-2-22-222-2-22i2i−2i−2i-22-2200000000−2i2i0000000000000000-2-22-222-22-2-222−2i−2i2i2i2-22-2000000002i−2i0000000000000000
χ7422-22-2-22-222-2-2−2i−2i2i2i-22-22000000002i−2i0000000000000000-2-22-222-22-2-2222i2i−2i−2i2-22-200000000−2i2i0000000000000000
χ7522-22-2-22-2-2-222000022-2-20000002i−2i0000−2i2i000000000000-2-22-222-2222-2-20000-2-222000000−2i2i00002i−2i000000000000
χ7622-22-2-22-2-2-222000022-2-2000000−2i2i00002i−2i000000000000-2-22-222-2222-2-20000-2-2220000002i−2i0000−2i2i000000000000
χ7722-22-2-22-2-2-2220000-2-22200002-20000-2200000000000000-2-22-222-2222-2-2000022-2-20000-2200002-200000000000000
χ7822-22-2-22-2-2-2220000-2-2220000-2200002-200000000000000-2-22-222-2222-2-2000022-2-200002-20000-2200000000000000
χ7922-2-2-22-222-22-22i−2i−2i2i0000000000000000000000i2−i2−i2i2−222−2-2-2222-22-2-22-22−2i2i2i−2i0000000000000000000000−i2i2i2−i22−2−22
χ8022-2-2-22-222-22-22i−2i−2i2i0000000000000000000000−i2i2i2−i22−2−22-2-2222-22-2-22-22−2i2i2i−2i0000000000000000000000i2−i2−i2i2−222−2
χ8122-2-2-22-222-22-2−2i2i2i−2i0000000000000000000000i2−i2−i2i22−2−22-2-2222-22-2-22-222i−2i−2i2i0000000000000000000000−i2i2i2−i2−222−2
χ8222-2-2-22-222-22-2−2i2i2i−2i0000000000000000000000−i2i2i2−i2−222−2-2-2222-22-2-22-222i−2i−2i2i0000000000000000000000i2−i2−i2i22−2−22
χ83444-44-4-4-4-444-40000000000000000000000000000000000-4-4-44-44444-4-440000000000000000000000000000000000
χ8444-4-4-44-44-44-440000000000000000000000000000000000-4-4444-44-44-44-40000000000000000000000000000000000
χ854-444-44-4-4000000000000000000000000002i−2i2i−2i00000000-44-4-44-44400000000000000000000000000−2i2i−2i2i00000000
χ864-444-44-4-400000000000000000000000000−2i2i−2i2i00000000-44-4-44-444000000000000000000000000002i−2i2i−2i00000000
χ874-44-4-4-4440000000000002-22-20000000000000000000000-44-4444-4-4000000000000-22-220000000000000000000000
χ884-44-4-4-444000000000000-22-220000000000000000000000-44-4444-4-40000000000002-22-20000000000000000000000
χ894-4-444-4-44000000000000000000000000002-2-2200000000-444-4-444-400000000000000000000000000-222-200000000
χ904-4-444-4-4400000000000000000000000000-222-200000000-444-4-444-4000000000000000000000000002-2-2200000000
χ914-4-4-4444-40000000000002-2-220000000000000000000000-4444-4-4-44000000000000-222-20000000000000000000000
χ924-4-4-4444-4000000000000-222-20000000000000000000000-4444-4-4-440000000000002-2-220000000000000000000000

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