Finite Group Databasebeta

← Group #366313

Character table — Group #366313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12222222222222222222444444442222444444444444444444444444222244444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-111111111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-11111-1-11111-1-1-1-111-1-1-1-111
χ1711-11-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i1-11-1i−ii−ii−ii−i1-11-1i−ii−i11-1-1ii−i−i1-1i−i1-1i−i
χ1811-11-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−i11-1-11111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i-11-11i−i−ii−iii−i-11-11−ii−ii11-1-1ii−i−i-11−ii-11−ii
χ1911-11-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−i11-1-1-1-1-1-11111ii−i−i11-1-1−i−i−i−iiiii1-11-1i−ii−ii−ii−i1-11-1i−ii−i-1-111−i−iii-11−ii-11−ii
χ2011-11-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−i11-1-1-1-1-1-11111ii−i−i11-1-1−i−i−i−iiiii-11-11i−i−ii−iii−i-11-11−ii−ii-1-111−i−iii1-1i−i1-1i−i
χ2111-11-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−i-1-1111111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i1-1-11−iii−i−ii−ii1-1-11i−i−ii-1-111−i−iii1-1i−i-11−ii
χ2211-11-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−i-1-1111111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i-111-1−ii−iii−i−ii-111-1−iii−i-1-111−i−iii-11−ii1-1i−i
χ2311-11-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−i-1-111-1-1-1-11111ii−i−i-1-111−i−i−i−iiiii1-1-11−iii−i−ii−ii1-1-11i−i−ii11-1-1ii−i−i-11−ii1-1i−i
χ2411-11-11-1-1111-1-1-1111-1-1-1iiii−i−i−i−i-1-111-1-1-1-11111ii−i−i-1-111−i−i−i−iiiii-111-1−ii−iii−i−ii-111-1−iii−i11-1-1ii−i−i1-1i−i-11−ii
χ2511-11-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1-11-1−ii−ii−ii−ii1-11-1−ii−ii11-1-1−i−iii1-1−ii1-1−ii
χ2611-11-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii-11-11−iii−ii−i−ii-11-11i−ii−i11-1-1−i−iii-11i−i-11i−i
χ2711-11-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii11-1-1-1-1-1-11111−i−iii11-1-1iiii−i−i−i−i1-11-1−ii−ii−ii−ii1-11-1−ii−ii-1-111ii−i−i-11i−i-11i−i
χ2811-11-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii11-1-1-1-1-1-11111−i−iii11-1-1iiii−i−i−i−i-11-11−iii−ii−i−ii-11-11i−ii−i-1-111ii−i−i1-1−ii1-1−ii
χ2911-11-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii-1-1111111-1-1-1-1−i−iii-1-111−i−i−i−iiiii1-1-11i−i−iii−ii−i1-1-11−iii−i-1-111ii−i−i1-1−ii-11i−i
χ3011-11-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii-1-1111111-1-1-1-1−i−iii-1-111−i−i−i−iiiii-111-1i−ii−i−iii−i-111-1i−i−ii-1-111ii−i−i-11i−i1-1−ii
χ3111-11-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii-1-111-1-1-1-11111−i−iii-1-111iiii−i−i−i−i1-1-11i−i−iii−ii−i1-1-11−iii−i11-1-1−i−iii-11i−i1-1−ii
χ3211-11-11-1-1111-1-1-1111-1-1-1−i−i−i−iiiii-1-111-1-1-1-11111−i−iii-1-111iiii−i−i−i−i-111-1i−ii−i−iii−i-111-1i−i−ii11-1-1−i−iii1-1−ii-11i−i
χ33222222222-2-22-2-22-2-22-2-222222222222200000000-2-2-2-2-2-2-2-2000000000000-2-2000022000000000000000000000000
χ34222222222-2-22-2-22-2-22-2-222222222-2-2-2-200000000-2-2-2-22222000000000000220000-2-2000000000000000000000000
χ35222222222-2-22-2-22-2-22-2-2-2-2-2-2-2-2-2-22222000000002222-2-2-2-2000000000000220000-2-2000000000000000000000000
χ36222222222-2-22-2-22-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022222222000000000000-2-2000022000000000000000000000000
χ3722222222-22-2-22-2-22-2-22-222-2-222-2-20000000000002-22-200000000000000220000220000-2-200-2-20000000000000000
χ3822222222-22-2-22-2-22-2-22-222-2-222-2-20000000000002-22-200000000000000-2-20000-2-200002200220000000000000000
χ3922222222-22-2-22-2-22-2-22-2-2-222-2-222000000000000-22-2200000000000000220000-2-20000-2-200220000000000000000
χ4022222222-22-2-22-2-22-2-22-2-2-222-2-222000000000000-22-2200000000000000-2-200002200002200-2-20000000000000000
χ4122222222-2-22-2-22-2-22-2-2222-2-222-2-2000000000000-22-22000000000000220000220000-2-200-2-2000000000000000000
χ4222222222-2-22-2-22-2-22-2-2222-2-222-2-2000000000000-22-22000000000000-2-20000-2-20000220022000000000000000000
χ4322222222-2-22-2-22-2-22-2-22-2-222-2-2220000000000002-22-2000000000000220000-2-20000-2-20022000000000000000000
χ4422222222-2-22-2-22-2-22-2-22-2-222-2-2220000000000002-22-2000000000000-2-200002200002200-2-2000000000000000000
χ4522-22-22-2-22-2-2-2222-2-2-2222i2i2i2i−2i−2i−2i−2i22-2-200000000−2i−2i2i2i-2-222000000000000−2i2i00002i−2i000000000000000000000000
χ4622-22-22-2-22-2-2-2222-2-2-2222i2i2i2i−2i−2i−2i−2i-2-22200000000−2i−2i2i2i22-2-20000000000002i−2i0000−2i2i000000000000000000000000
χ4722-22-22-2-22-2-2-2222-2-2-222−2i−2i−2i−2i2i2i2i2i22-2-2000000002i2i−2i−2i-2-2220000000000002i−2i0000−2i2i000000000000000000000000
χ4822-22-22-2-22-2-2-2222-2-2-222−2i−2i−2i−2i2i2i2i2i-2-222000000002i2i−2i−2i22-2-2000000000000−2i2i00002i−2i000000000000000000000000
χ4922-22-22-2-2-22-22-22-22-22-222i2i−2i−2i−2i−2i2i2i0000000000002i−2i−2i2i000000000000002-200002i−2i0000-2200−2i2i0000000000000000
χ5022-22-22-2-2-22-22-22-22-22-222i2i−2i−2i−2i−2i2i2i0000000000002i−2i−2i2i00000000000000-220000−2i2i00002-2002i−2i0000000000000000
χ5122-22-22-2-2-22-22-22-22-22-22−2i−2i2i2i2i2i−2i−2i000000000000−2i2i2i−2i000000000000002-20000−2i2i0000-22002i−2i0000000000000000
χ5222-22-22-2-2-22-22-22-22-22-22−2i−2i2i2i2i2i−2i−2i000000000000−2i2i2i−2i00000000000000-2200002i−2i00002-200−2i2i0000000000000000
χ5322-22-22-2-2-2-2222-2-2-2222-22i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i0000000000002-200002i−2i0000-2200−2i2i000000000000000000
χ5422-22-22-2-2-2-2222-2-2-2222-22i2i−2i−2i−2i−2i2i2i000000000000−2i2i2i−2i000000000000-220000−2i2i00002-2002i−2i000000000000000000
χ5522-22-22-2-2-2-2222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i0000000000002-20000−2i2i0000-22002i−2i000000000000000000
χ5622-22-22-2-2-2-2222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i0000000000002i−2i−2i2i000000000000-2200002i−2i00002-200−2i2i000000000000000000
χ572-22-2-222-22222-2-2-2-2-2-222000000002-22-22i2i−2i−2i2i2i−2i−2i00002-22-200000000000000000000000000002i−2i2i−2i000000000000
χ582-22-2-222-22222-2-2-2-2-2-222000000002-22-2−2i−2i2i2i−2i−2i2i2i00002-22-20000000000000000000000000000−2i2i−2i2i000000000000
χ592-22-2-222-22222-2-2-2-2-2-22200000000-22-222i2i−2i−2i2i2i−2i−2i0000-22-220000000000000000000000000000−2i2i−2i2i000000000000
χ602-22-2-222-22222-2-2-2-2-2-22200000000-22-22−2i−2i2i2i−2i−2i2i2i0000-22-2200000000000000000000000000002i−2i2i−2i000000000000
χ612-22-2-222-22-2-2222-222-2-2-2000000002-22-2000000000000-22-222i2i−2i−2i2i2i−2i−2i0000000000000000000000002i−2i2i−2i00000000
χ622-22-2-222-22-2-2222-222-2-2-2000000002-22-2000000000000-22-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000−2i2i−2i2i00000000
χ632-22-2-222-22-2-2222-222-2-2-200000000-22-220000000000002-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000−2i2i−2i2i00000000
χ642-22-2-222-22-2-2222-222-2-2-200000000-22-220000000000002-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000002i−2i2i−2i00000000
χ652-2-2-222-22222-222-2-2-22-2-2000000002-2-222i2i−2i−2i−2i−2i2i2i00002-2-2200000000000000000000000000002i−2i−2i2i000000000000
χ662-2-2-222-22222-222-2-2-22-2-2000000002-2-22−2i−2i2i2i2i2i−2i−2i00002-2-220000000000000000000000000000−2i2i2i−2i000000000000
χ672-2-2-222-22222-222-2-2-22-2-200000000-222-22i2i−2i−2i−2i−2i2i2i0000-222-20000000000000000000000000000−2i2i2i−2i000000000000
χ682-2-2-222-22222-222-2-2-22-2-200000000-222-2−2i−2i2i2i2i2i−2i−2i0000-222-200000000000000000000000000002i−2i−2i2i000000000000
χ692-2-2-222-222-2-2-2-2-2-222222000000002-2-22000000000000-222-222-2-2-2-2220000000000000000000000002-2-2200000000
χ702-2-2-222-222-2-2-2-2-2-222222000000002-2-22000000000000-222-2-2-22222-2-2000000000000000000000000-222-200000000
χ712-2-2-222-222-2-2-2-2-2-22222200000000-222-20000000000002-2-2222-2-2-2-222000000000000000000000000-222-200000000
χ722-2-2-222-222-2-2-2-2-2-22222200000000-222-20000000000002-2-22-2-22222-2-20000000000000000000000002-2-2200000000
χ73444-4-4-4-440000000000004i−4i004i−4i0000002i−2i2i−2i2i−2i2i−2i000000002-22-22-22-2000000000000000000000000000000000000
χ74444-4-4-4-440000000000004i−4i004i−4i000000−2i2i−2i2i−2i2i−2i2i00000000-22-22-22-22000000000000000000000000000000000000
χ75444-4-4-4-44000000000000−4i4i00−4i4i0000002i−2i2i−2i2i−2i2i−2i00000000-22-22-22-22000000000000000000000000000000000000
χ76444-4-4-4-44000000000000−4i4i00−4i4i000000−2i2i−2i2i−2i2i−2i2i000000002-22-22-22-2000000000000000000000000000000000000
χ7744-4-44-44-40000000000004-400-440000002i−2i2i−2i−2i2i−2i2i00000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ7844-4-44-44-40000000000004-400-44000000−2i2i−2i2i2i−2i2i−2i000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ7944-4-44-44-4000000000000-44004-40000002i−2i2i−2i−2i2i−2i2i000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ8044-4-44-44-4000000000000-44004-4000000−2i2i−2i2i2i−2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ814-4444-4-4-4000000000000004i−4i004i−4i00002-2-222-2-22000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ824-4444-4-4-4000000000000004i−4i004i−4i0000-222-2-222-200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ834-4444-4-4-400000000000000−4i4i00−4i4i00002-2-222-2-2200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ844-4444-4-4-400000000000000−4i4i00−4i4i0000-222-2-222-2000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ854-44-4-444-4-44-4-4-444-4444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ864-44-4-444-4-4-44-44-444-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ874-4-44-4-444000000000000004-400-4400002-2-22-222-2000000002-2-22-222-2000000000000000000000000000000000000
χ884-4-44-4-444000000000000004-400-440000-222-22-2-2200000000-222-22-2-22000000000000000000000000000000000000
χ894-4-44-4-44400000000000000-44004-400002-2-22-222-200000000-222-22-2-22000000000000000000000000000000000000
χ904-4-44-4-44400000000000000-44004-40000-222-22-2-22000000002-2-22-222-2000000000000000000000000000000000000
χ914-4-4-444-44-44-444-44-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-444-44-4-444-4444-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000

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