Finite Group Databasebeta

← Group #192063

Character table — Group #192063

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111111222244444444888888888888888888888888881111111122224444444488888888888888888888888888
order12222222222244444444444444444444444444888888882222222222224444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911-111-1-1-111-1-111-1-1-1-1111-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-111-1-1-111-1-111-1-1-1-1111-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1011-111-1-1-111-1-111-1-1-1-1111-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-11111-111-1-1-111-1-111-1-1-1-1111-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ1111-111-1-1-111-1-111-1-1-1-1111-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-11111-111-1-1-111-1-111-1-1-1-1111-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ1211-111-1-1-111-1-111-1-1-1-1111-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-111-1-1-111-1-111-1-1-1-1111-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1311-111-1-1-111-1-1-1-111-1-111-11ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-11111-111-1-1-111-1-1-1-111-1-111-11ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ1411-111-1-1-111-1-1-1-111-1-111-11ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-111-111-1-1-111-1-1-1-111-1-111-11ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ1511-111-1-1-111-1-1-1-111-1-111-11−i−iiiii−i−iii−i−i−i−iii-1-11111-1-111-111-1-1-111-1-1-1-111-1-111-11−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ1611-111-1-1-111-1-1-1-111-1-111-11−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-11111-111-1-1-111-1-1-1-111-1-111-11−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ172222222222222222-2-2-2-2-2-20000000000000000000000002222222222222222-2-2-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-222000000000000000000000000222222222222-2-2-2-2-2-2-2-222000000000000000000000000
χ1922222222-2-2-2-200002-22-20000002-22-2000000000000000022222222-2-2-2-200002-22-20000002-22-20000000000000000
χ2022222222-2-2-2-200002-22-2000000-22-22000000000000000022222222-2-2-2-200002-22-2000000-22-220000000000000000
χ2122222222-2-2-2-20000-22-22002-22-20000000000000000000022222222-2-2-2-20000-22-22002-22-200000000000000000000
χ2222222222-2-2-2-20000-22-2200-22-220000000000000000000022222222-2-2-2-20000-22-2200-22-2200000000000000000000
χ2322-222-2-2-222-2-222-2-222-2-2-2200000000000000000000000022-222-2-2-222-2-222-2-222-2-2-22000000000000000000000000
χ2422-222-2-2-222-2-2-2-22222-2-22-200000000000000000000000022-222-2-2-222-2-2-2-22222-2-22-2000000000000000000000000
χ2522-222-2-2-2-2-22200002-2-22002i−2i−2i2i0000000000000000000022-222-2-2-2-2-22200002-2-22002i−2i−2i2i00000000000000000000
χ2622-222-2-2-2-2-22200002-2-2200−2i2i2i−2i0000000000000000000022-222-2-2-2-2-22200002-2-2200−2i2i2i−2i00000000000000000000
χ2722-222-2-2-2-2-2220000-222-20000002i−2i−2i2i000000000000000022-222-2-2-2-2-2220000-222-20000002i−2i−2i2i0000000000000000
χ2822-222-2-2-2-2-2220000-222-2000000−2i2i2i−2i000000000000000022-222-2-2-2-2-2220000-222-2000000−2i2i2i−2i0000000000000000
χ292-222-22-2-22-2-222-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i22-222-22-2-22-2-222-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ302-222-22-2-22-2-222-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i22-222-22-2-22-2-222-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ312-222-22-2-22-2-22-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i22-222-22-2-22-2-22-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ322-222-22-2-22-2-22-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i22-222-22-2-22-2-22-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ332-2-22-2-2222-22-22-2-220000000000000000000000i2−i2−i2i2i2−i2−i2i22-2-22-2-2222-22-22-2-220000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ342-2-22-2-2222-22-22-2-220000000000000000000000−i2i2i2−i2−i2i2i2−i22-2-22-2-2222-22-22-2-220000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ352-2-22-2-2222-22-2-222-20000000000000000000000i2−i2−i2i2−i2i2i2−i22-2-22-2-2222-22-2-222-20000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ362-2-22-2-2222-22-2-222-20000000000000000000000−i2i2i2−i2i2−i2−i2i22-2-22-2-2222-22-2-222-20000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ37444-4-4-44-4000000000000000000000000002-22-200000000444-4-4-44-4000000000000000000000000002-22-200000000
χ38444-4-4-44-400000000000000000000000000-22-2200000000444-4-4-44-400000000000000000000000000-22-2200000000
χ3944-4-4-44-44000000000000000000000000002i−2i−2i2i0000000044-4-4-44-44000000000000000000000000002i−2i−2i2i00000000
χ4044-4-4-44-4400000000000000000000000000−2i2i2i−2i0000000044-4-4-44-4400000000000000000000000000−2i2i2i−2i00000000
χ414-444-44-4-4-444-400000000000000000000000000000000004-444-44-4-4-444-40000000000000000000000000000000000
χ424-44-44-4-4400000000000000000000002i−2i2i−2i0000000000004-44-44-4-4400000000000000000000002i−2i2i−2i000000000000
χ434-44-44-4-440000000000000000000000−2i2i−2i2i0000000000004-44-44-4-440000000000000000000000−2i2i−2i2i000000000000
χ444-4-44-4-444-44-4400000000000000000000000000000000004-4-44-4-444-44-440000000000000000000000000000000000
χ454-4-4-4444-400000000000000000000002-2-220000000000004-4-4-4444-400000000000000000000002-2-22000000000000
χ464-4-4-4444-40000000000000000000000-222-20000000000004-4-4-4444-40000000000000000000000-222-2000000000000
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
χ48111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ491111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ501111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ51111111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ52111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ53111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ54111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5511-111-1-1-111-1-111-1-1-1-1111-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1-1-11-1-1111-1-111-1-11111-1-1-11−i−iii−i−iii−i−iii−i−iii-1-111-1-111
χ5611-111-1-1-111-1-111-1-1-1-1111-1ii−i−iii−i−i−i−iii−i−iii-1-111-1-111-1-11-1-1111-1-111-1-11111-1-1-11−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1
χ5711-111-1-1-111-1-111-1-1-1-1111-1−i−iii−i−iiiii−i−iii−i−i-1-111-1-111-1-11-1-1111-1-111-1-11111-1-1-11ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1
χ5811-111-1-1-111-1-111-1-1-1-1111-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1-1-11-1-1111-1-111-1-11111-1-1-11ii−i−iii−i−iii−i−iii−i−i-1-111-1-111
χ5911-111-1-1-111-1-1-1-111-1-111-11ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111-1-11-1-1111-1-11111-1-111-1-11-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ6011-111-1-1-111-1-1-1-111-1-111-11ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1-1-11-1-1111-1-11111-1-111-1-11-1−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ6111-111-1-1-111-1-1-1-111-1-111-11−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1-1-11-1-1111-1-11111-1-111-1-11-1ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ6211-111-1-1-111-1-1-1-111-1-111-11−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111-1-11-1-1111-1-11111-1-111-1-11-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ632222222222222222-2-2-2-2-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000
χ64222222222222-2-2-2-2-2-2-2-222000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2000000000000000000000000
χ6522222222-2-2-2-200002-22-20000002-22-20000000000000000-2-2-2-2-2-2-2-222220000-22-22000000-22-220000000000000000
χ6622222222-2-2-2-200002-22-2000000-22-220000000000000000-2-2-2-2-2-2-2-222220000-22-220000002-22-20000000000000000
χ6722222222-2-2-2-20000-22-22002-22-200000000000000000000-2-2-2-2-2-2-2-2222200002-22-200-22-2200000000000000000000
χ6822222222-2-2-2-20000-22-2200-22-2200000000000000000000-2-2-2-2-2-2-2-2222200002-22-2002-22-200000000000000000000
χ6922-222-2-2-222-2-222-2-222-2-2-22000000000000000000000000-2-22-2-2222-2-222-2-222-2-2222-2000000000000000000000000
χ7022-222-2-2-222-2-2-2-22222-2-22-2000000000000000000000000-2-22-2-2222-2-22222-2-2-2-222-22000000000000000000000000
χ7122-222-2-2-2-2-22200002-2-22002i−2i−2i2i00000000000000000000-2-22-2-222222-2-20000-222-200−2i2i2i−2i00000000000000000000
χ7222-222-2-2-2-2-22200002-2-2200−2i2i2i−2i00000000000000000000-2-22-2-222222-2-20000-222-2002i−2i−2i2i00000000000000000000
χ7322-222-2-2-2-2-2220000-222-20000002i−2i−2i2i0000000000000000-2-22-2-222222-2-200002-2-22000000−2i2i2i−2i0000000000000000
χ7422-222-2-2-2-2-2220000-222-2000000−2i2i2i−2i0000000000000000-2-22-2-222222-2-200002-2-220000002i−2i−2i2i0000000000000000
χ752-222-22-2-22-2-222-22-20000000000000000000000i2−i2i2−i2i2−i2i2−i2-22-2-22-222-222-2-22-220000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ762-222-22-2-22-2-222-22-20000000000000000000000−i2i2−i2i2−i2i2−i2i2-22-2-22-222-222-2-22-220000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ772-222-22-2-22-2-22-22-220000000000000000000000i2−i2i2−i2−i2i2−i2i2-22-2-22-222-222-22-22-20000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ782-222-22-2-22-2-22-22-220000000000000000000000−i2i2−i2i2i2−i2i2−i2-22-2-22-222-222-22-22-20000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ792-2-22-2-2222-22-22-2-220000000000000000000000i2−i2−i2i2i2−i2−i2i2-222-222-2-2-22-22-222-20000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ802-2-22-2-2222-22-22-2-220000000000000000000000−i2i2i2−i2−i2i2i2−i2-222-222-2-2-22-22-222-20000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ812-2-22-2-2222-22-2-222-20000000000000000000000i2−i2−i2i2−i2i2i2−i2-222-222-2-2-22-222-2-220000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ822-2-22-2-2222-22-2-222-20000000000000000000000−i2i2i2−i2i2−i2−i2i2-222-222-2-2-22-222-2-220000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ83444-4-4-44-4000000000000000000000000002-22-200000000-4-4-4444-4400000000000000000000000000-22-2200000000
χ84444-4-4-44-400000000000000000000000000-22-2200000000-4-4-4444-44000000000000000000000000002-22-200000000
χ8544-4-4-44-44000000000000000000000000002i−2i−2i2i00000000-4-4444-44-400000000000000000000000000−2i2i2i−2i00000000
χ8644-4-4-44-4400000000000000000000000000−2i2i2i−2i00000000-4-4444-44-4000000000000000000000000002i−2i−2i2i00000000
χ874-444-44-4-4-444-40000000000000000000000000000000000-44-4-44-4444-4-440000000000000000000000000000000000
χ884-44-44-4-4400000000000000000000002i−2i2i−2i000000000000-44-44-444-40000000000000000000000−2i2i−2i2i000000000000
χ894-44-44-4-440000000000000000000000−2i2i−2i2i000000000000-44-44-444-400000000000000000000002i−2i2i−2i000000000000
χ904-4-44-4-444-44-440000000000000000000000000000000000-444-444-4-44-44-40000000000000000000000000000000000
χ914-4-4-4444-400000000000000000000002-2-22000000000000-4444-4-4-440000000000000000000000-222-2000000000000
χ924-4-4-4444-40000000000000000000000-222-2000000000000-4444-4-4-4400000000000000000000002-2-22000000000000

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