Finite Group Databasebeta

← Group #194147

Character table — Group #194147

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444422444444444444444444444444444444444444888888888888888822448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-11-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-111
χ111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ121111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ131111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111111-1-1-1-11-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ141111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111111-1-1-1-11-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ151111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ161111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1711-1-11-1-111111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i1-111-1-1111-1-1-1i−ii−i1-1ii−i−iii−i−i1-1ii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ1811-1-11-1-111111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i1-111-1-1111-1-1-1i−ii−i1-1ii−i−iii−i−i1-1−i−iii−i−iii−i−iii−i−iii-11-11-11-11
χ1911-1-11-1-111111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i1-1-1-1111-1-111-1i−ii−i-11−i−iii−i−iii-11ii−i−iii−i−i−i−iii−i−iii1-11-1-11-11
χ2011-1-11-1-111111-1-1-1-111-1-1-1-1111-1ii−i−iii−i−i1-1-1-1111-1-111-1i−ii−i-11−i−iii−i−iii-11−i−iii−i−iiiii−i−iii−i−i-11-111-11-1
χ2111-1-11-1-111111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii1-111-1-1111-1-1-1−ii−ii1-1−i−iii−i−iii1-1ii−i−iii−i−iii−i−iii−i−i-11-11-11-11
χ2211-1-11-1-111111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii1-111-1-1111-1-1-1−ii−ii1-1−i−iii−i−iii1-1−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ2311-1-11-1-111111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii1-1-1-1111-1-111-1−ii−ii-11ii−i−iii−i−i-11ii−i−iii−i−i−i−iii−i−iii-11-111-11-1
χ2411-1-11-1-111111-1-1-1-111-1-1-1-1111-1−i−iii−i−iii1-1-1-1111-1-111-1−ii−ii-11ii−i−iii−i−i-11−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11
χ2511-1-11-1-1111-1-111-1-1-1-111-1-111-11ii−i−i−i−iii-1111-1-11-1-111-1i−i−ii-11ii−i−i−i−iii1-1ii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11
χ2611-1-11-1-1111-1-111-1-1-1-111-1-111-11ii−i−i−i−iii-1111-1-11-1-111-1i−i−ii-11ii−i−i−i−iii1-1−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ2711-1-11-1-1111-1-111-1-1-1-111-1-111-11ii−i−i−i−iii-11-1-111111-1-1-1i−i−ii1-1−i−iiiii−i−i-11ii−i−i−i−iii−i−iiiii−i−i1-1-11-111-1
χ2811-1-11-1-1111-1-111-1-1-1-111-1-111-11ii−i−i−i−iii-11-1-111111-1-1-1i−i−ii1-1−i−iiiii−i−i-11−i−iiiii−i−iii−i−i−i−iii-111-11-1-11
χ2911-1-11-1-1111-1-111-1-1-1-111-1-111-11−i−iiiii−i−i-1111-1-11-1-111-1−iii−i-11−i−iiiii−i−i1-1ii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ3011-1-11-1-1111-1-111-1-1-1-111-1-111-11−i−iiiii−i−i-1111-1-11-1-111-1−iii−i-11−i−iiiii−i−i1-1−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11
χ3111-1-11-1-1111-1-111-1-1-1-111-1-111-11−i−iiiii−i−i-11-1-111111-1-1-1−iii−i1-1ii−i−i−i−iii-11ii−i−i−i−iii−i−iiiii−i−i-111-11-1-11
χ3211-1-11-1-1111-1-111-1-1-1-111-1-111-11−i−iiiii−i−i-11-1-111111-1-1-1−iii−i1-1ii−i−i−i−iii-11−i−iiiii−i−iii−i−i−i−iii1-1-11-111-1
χ3322222222222222-2-2-2-2-2-222-2-22222222222-2-20000-20000-2-2-2-2-2000000000000000000000000000000000000
χ3422222222222222-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-20000-20000-22222000000000000000000000000000000000000
χ352222222222-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2220000-20000-2-2-222000000000000000000000000000000000000
χ362222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222220000-20000-222-2-2000000000000000000000000000000000000
χ3722222222-2-22222222222-2-222-2-200000000-2-22222-22222-20000-2-200000000-2-2000000000000000000000000
χ3822222222-2-22222222222-2-222-2-200000000-2-2-2-2-2-2-2-2-2-2-2-20000220000000022000000000000000000000000
χ3922222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000002200002000020000002-22-22-22-200000000000000000000000000
χ4022222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000220000200002000000-22-22-22-2200000000000000000000000000
χ4122222222-2-2-2-2-2-222-2-2-2-2-2-2222200000000222222-2-2-2-2-2-200002200000000-2-2000000000000000000000000
χ4222222222-2-2-2-2-2-222-2-2-2-2-2-222220000000022-2-2-2-2-22222-20000-2-20000000022000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-22222-2-2-2-22200000000-2-200002000020000002-22-2-22-2200000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-22222-2-2-2-22200000000-2-20000200002000000-22-222-22-200000000000000000000000000
χ4522-2-22-2-222222-2-222-2-222-2-2-2-22-22i2i−2i−2i2i2i−2i−2i-220000-200002−2i2i−2i2i000000000000000000000000000000000000
χ4622-2-22-2-222222-2-222-2-222-2-2-2-22-2−2i−2i2i2i−2i−2i2i2i-220000-2000022i−2i2i−2i000000000000000000000000000000000000
χ4722-2-22-2-2222-2-2222222-2-2-2-2-2-2-222i2i−2i−2i−2i−2i2i2i2-20000-200002−2i2i2i−2i000000000000000000000000000000000000
χ4822-2-22-2-2222-2-2222222-2-2-2-2-2-2-22−2i−2i2i2i2i2i−2i−2i2-20000-2000022i−2i−2i2i000000000000000000000000000000000000
χ4922-2-22-2-22-2-222-2-222-2-22222-2-2-22000000002-2000020000-20000002i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ5022-2-22-2-22-2-222-2-222-2-22222-2-2-22000000002-2000020000-2000000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ5122-2-22-2-22-2-222-2-2-2-222-2-22222-2200000000-2222-2-2-222-2-220000-2200000000-22000000000000000000000000
χ5222-2-22-2-22-2-222-2-2-2-222-2-22222-2200000000-22-2-222-2-2-222200002-2000000002-2000000000000000000000000
χ5322-2-22-2-22-2-2-2-2222222-2-222-2-22-200000000-22000020000-20000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ5422-2-22-2-22-2-2-2-2222222-2-222-2-22-200000000-22000020000-2000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ5522-2-22-2-22-2-2-2-222-2-2-2-22222222-2000000002-222-2-2-2-2-222200002-200000000-22000000000000000000000000
χ5622-2-22-2-22-2-2-2-222-2-2-2-22222222-2000000002-2-2-222-222-2-220000-22000000002-2000000000000000000000000
χ572-22-222-2-2002i−2i2i−2i2-22i−2i2i−2i002-20000000000002-22-202i−2i2i−2i000000000000000002−22−2i2−i2i2−i22−22−2i2−i2i2−i200000000
χ582-22-222-2-2002i−2i2i−2i2-22i−2i2i−2i002-20000000000002-22-202i−2i2i−2i00000000000000000−22−22−i2i2−i2i2−22−22−i2i2−i2i200000000
χ592-22-222-2-2002i−2i2i−2i2-22i−2i2i−2i002-2000000000000-22-220−2i2i−2i2i000000000000000002−22−2i2−i2i2−i2−22−22−i2i2−i2i200000000
χ602-22-222-2-2002i−2i2i−2i2-22i−2i2i−2i002-2000000000000-22-220−2i2i−2i2i00000000000000000−22−22−i2i2−i2i22−22−2i2−i2i2−i200000000
χ612-22-222-2-200−2i2i−2i2i2-2−2i2i−2i2i002-20000000000002-22-20−2i2i−2i2i000000000000000002−22−2−i2i2−i2i22−22−2−i2i2−i2i200000000
χ622-22-222-2-200−2i2i−2i2i2-2−2i2i−2i2i002-20000000000002-22-20−2i2i−2i2i00000000000000000−22−22i2−i2i2−i2−22−22i2−i2i2−i200000000
χ632-22-222-2-200−2i2i−2i2i2-2−2i2i−2i2i002-2000000000000-22-2202i−2i2i−2i000000000000000002−22−2−i2i2−i2i2−22−22i2−i2i2−i200000000
χ642-22-222-2-200−2i2i−2i2i2-2−2i2i−2i2i002-2000000000000-22-2202i−2i2i−2i00000000000000000−22−22i2−i2i2−i22−22−2−i2i2−i2i200000000
χ652-2-222-22-2002i−2i−2i2i-222i−2i−2i2i002-20000000000002-2-2202i−2i−2i2i00000000000000000i2−i2−i2i2−222−2i2−i2−i2i2−222−200000000
χ662-2-222-22-2002i−2i−2i2i-222i−2i−2i2i002-20000000000002-2-2202i−2i−2i2i00000000000000000−i2i2i2−i22−2−22−i2i2i2−i22−2−2200000000
χ672-2-222-22-2002i−2i−2i2i-222i−2i−2i2i002-2000000000000-222-20−2i2i2i−2i00000000000000000i2−i2−i2i2−222−2−i2i2i2−i22−2−2200000000
χ682-2-222-22-2002i−2i−2i2i-222i−2i−2i2i002-2000000000000-222-20−2i2i2i−2i00000000000000000−i2i2i2−i22−2−22i2−i2−i2i2−222−200000000
χ692-2-222-22-200−2i2i2i−2i-22−2i2i2i−2i002-20000000000002-2-220−2i2i2i−2i00000000000000000i2−i2−i2i22−2−22i2−i2−i2i22−2−2200000000
χ702-2-222-22-200−2i2i2i−2i-22−2i2i2i−2i002-20000000000002-2-220−2i2i2i−2i00000000000000000−i2i2i2−i2−222−2−i2i2i2−i2−222−200000000
χ712-2-222-22-200−2i2i2i−2i-22−2i2i2i−2i002-2000000000000-222-202i−2i−2i2i00000000000000000i2−i2−i2i22−2−22−i2i2i2−i2−222−200000000
χ722-2-222-22-200−2i2i2i−2i-22−2i2i2i−2i002-2000000000000-222-202i−2i−2i2i00000000000000000−i2i2i2−i2−222−2i2−i2−i2i22−2−2200000000
χ734444-4-4-4-44-400000000004-4000000004-44-40000000000000000000000000000000000000000000000000000
χ744444-4-4-4-44-400000000004-400000000-44-440000000000000000000000000000000000000000000000000000
χ754444-4-4-4-4-440000000000-4400004-44-400000000000000000000000000000000000000000000000000000000
χ764444-4-4-4-4-440000000000-440000-44-4400000000000000000000000000000000000000000000000000000000
χ7744-4-4-444-44-40000000000-44000000004i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ7844-4-4-444-44-40000000000-4400000000−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ7944-4-4-444-4-4400000000004-400004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ8044-4-4-444-4-4400000000004-40000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ814-44-444-4-4004i−4i4i−4i-44−4i4i−4i4i00-4400000000000000000000000000000000000000000000000000000000000000
χ824-44-444-4-400−4i4i−4i4i-444i−4i4i−4i00-4400000000000000000000000000000000000000000000000000000000000000
χ834-4-444-44-4004i−4i−4i4i4-4−4i4i4i−4i00-4400000000000000000000000000000000000000000000000000000000000000
χ844-4-444-44-400−4i4i4i−4i4-44i−4i−4i4i00-4400000000000000000000000000000000000000000000000000000000000000
χ858-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-88-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000

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