Finite Group Databasebeta

← Group #10944159

Character table — Group #10944159

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order1222223444444666666622224444444121212121212121244446666121212121212121212121212121222224444444444442266668888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1111111-1-111
χ811111111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111111-1-1
χ9111111111-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11-111-1-11-11-1
χ10111111111-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-111-1-1-11-11
χ11111111111-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-11-1-111-11-11
χ12111111111-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-11-1-1111-11-1
χ13111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111-11-1-1111-1-11
χ14111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1-11-1-111-111-1
χ15111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1111-111-1-1-111-1
χ16111111111-1-1111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-11-111-1-11-1-11
χ172222222-2-222-2-2222222222-2-2-2-2222-2-2-2-2-2-22222000022-2-2-2-20000000022-2-200000000000000000000000000
χ182222222-2-222-2-22222222-2-222-2-22-2-222-2-2-2-222220000-2-222-2-200000000-2-22200000000000000000000000000
χ192222222-2-2-2-2-2-2222222222-2-222-2-2-222-2-2-2-2-2-2-2-2000022-2-22200000000-2-22200000000000000000000000000
χ202222222-2-2-2-2-2-22222222-2-22222-222-2-2-2-2-2-2-2-2-2-20000-2-222220000000022-2-200000000000000000000000000
χ21222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ22222222-1222222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-1-1-1-10000000000000000-2-211110000
χ23222222-1222222-1-1-1-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-122221111-1-1-1-1-1-1-1-1-1-111110000000000000000-2-211110000
χ24222222-1222222-1-1-1-1-1-1-1-2-2-2-2222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111111111111000000000000000022-1-1-1-10000
χ25222222-122-2-222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-1-1-1-1111122-2-2-1-1-1-111-1-1-1-11111111100000000000000002-2-1-1110000
χ26222222-122-2-222-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-1-1-1-11111-2-222-1-1-1-1111111-1-1-1-111110000000000000000-2211-1-10000
χ27222222-122-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-1-1111122-2-2111111-1-1-1-11111-1-1-1-10000000000000000-2211-1-10000
χ28222222-122-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-22222-1-1-1-11111-2-2221111111111-1-1-1-1-1-1-1-100000000000000002-2-1-1110000
χ29222222-1-2-222-2-2-1-1-1-1-1-1-122-2-2-2-2222-2-21111-1-1-1-10000-1-11111−i3−i3i3i3−i3−i3i3i3-1-111000000000000000000−i3i3−i3i30000
χ30222222-1-2-222-2-2-1-1-1-1-1-1-122-2-2-2-2222-2-21111-1-1-1-10000-1-11111i3i3−i3−i3i3i3−i3−i3-1-111000000000000000000i3−i3i3−i30000
χ31222222-1-2-222-2-2-1-1-1-1-1-1-1-2-222-2-22-2-2221111-1-1-1-1000011-1-111−i3−i3i3i3−i3−i3i3i311-1-1000000000000000000i3−i3i3−i30000
χ32222222-1-2-222-2-2-1-1-1-1-1-1-1-2-222-2-22-2-2221111-1-1-1-1000011-1-111i3i3−i3−i3i3i3−i3−i311-1-1000000000000000000−i3i3−i3i30000
χ33222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-222111111110000-1-111-1-1−i3−i3i3i3i3i3−i3−i311-1-1000000000000000000−i3i3i3−i30000
χ34222222-1-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222-2-2-222111111110000-1-111-1-1i3i3−i3−i3−i3−i3i3i311-1-1000000000000000000i3−i3−i3i30000
χ35222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-222-2-211111111000011-1-1-1-1−i3−i3i3i3i3i3−i3−i3-1-111000000000000000000i3−i3−i3i30000
χ36222222-1-2-2-2-2-2-2-1-1-1-1-1-1-1-2-22222-222-2-211111111000011-1-1-1-1i3i3−i3−i3−i3−i3i3i3-1-111000000000000000000−i3i3i3−i30000
χ372222-2-222-2222-2-2-222-2-2200002-2-2000022-2-222-2-2000000002-200000000000000220000-2-2-2-200220000000000
χ382222-2-222-2222-2-2-222-2-2200002-2-2000022-2-222-2-2000000002-200000000000000-2-20000222200-2-20000000000
χ392222-2-222-2-2-22-2-2-222-2-220000-222000022-2-2-2-22200000000-2200000000000000220000-2-22200-2-20000000000
χ402222-2-222-2-2-22-2-2-222-2-220000-222000022-2-2-2-22200000000-2200000000000000-2-2000022-2-200220000000000
χ412222-2-22-2222-22-2-222-2-220000-22-20000-2-22222-2-200000000-220000000000002200-2-2-2-2000022000000000000
χ422222-2-22-2222-22-2-222-2-220000-22-20000-2-22222-2-200000000-22000000000000-2-20022220000-2-2000000000000
χ432222-2-22-22-2-2-22-2-222-2-2200002-220000-2-222-2-222000000002-20000000000002200-2-2220000-2-2000000000000
χ442222-2-22-22-2-2-22-2-222-2-2200002-220000-2-222-2-222000000002-2000000000000-2-20022-2-2000022000000000000
χ4522-2-22-222-200-22222-2-2-2-200000002i−2i2i−2i2-22-200000000000000000000002i−2i2i−2i2-2002-200002i−2i002i−2i0000000000
χ4622-2-22-222-200-22222-2-2-2-200000002i−2i2i−2i2-22-200000000000000000000002i−2i2i−2i-2200-220000−2i2i00−2i2i0000000000
χ4722-2-22-222-200-22222-2-2-2-20000000−2i2i−2i2i2-22-20000000000000000000000−2i2i−2i2i2-2002-20000−2i2i00−2i2i0000000000
χ4822-2-22-222-200-22222-2-2-2-20000000−2i2i−2i2i2-22-20000000000000000000000−2i2i−2i2i-2200-2200002i−2i002i−2i0000000000
χ4922-2-22-22-22002-2222-2-2-2-200000002i−2i−2i2i-22-2200000000000000000000002i−2i−2i2i002-2002i−2i2-2002i−2i000000000000
χ5022-2-22-22-22002-2222-2-2-2-200000002i−2i−2i2i-22-2200000000000000000000002i−2i−2i2i00-2200−2i2i-2200−2i2i000000000000
χ5122-2-22-22-22002-2222-2-2-2-20000000−2i2i2i−2i-22-220000000000000000000000−2i2i2i−2i002-200−2i2i2-200−2i2i000000000000
χ5222-2-22-22-22002-2222-2-2-2-20000000−2i2i2i−2i-22-220000000000000000000000−2i2i2i−2i00-22002i−2i-22002i−2i000000000000
χ5322-2-2-2222200-2-2-2-22-222-22-22-200000002-2-22000000002-22-2000000000000000000002i−2i002i−2i−2i2i−2i2i0000000000
χ5422-2-2-2222200-2-2-2-22-222-22-22-200000002-2-22000000002-22-200000000000000000000−2i2i00−2i2i2i−2i2i−2i0000000000
χ5522-2-2-2222200-2-2-2-22-222-2-22-2200000002-2-2200000000-22-22000000000000000000002i−2i00−2i2i−2i2i2i−2i0000000000
χ5622-2-2-2222200-2-2-2-22-222-2-22-2200000002-2-2200000000-22-2200000000000000000000−2i2i002i−2i2i−2i−2i2i0000000000
χ5722-2-2-222-2-20022-2-22-222-22-2-220000000-222-2000000002-2-22000000000000002-22-2-2200-220000000000000000
χ5822-2-2-222-2-20022-2-22-222-22-2-220000000-222-2000000002-2-2200000000000000-22-222-2002-20000000000000000
χ5922-2-2-222-2-20022-2-22-222-2-222-20000000-222-200000000-222-2000000000000002-2-22-22002-20000000000000000
χ6022-2-2-222-2-20022-2-22-222-2-222-20000000-222-200000000-222-200000000000000-222-22-200-220000000000000000
χ614444-4-4-24-4444-422-2-222-200004-4-40000-2-222-2-22200000000-2200000000000000000000000000000000000000
χ624444-4-4-24-4-4-44-422-2-222-20000-4440000-2-22222-2-2000000002-200000000000000000000000000000000000000
χ634444-4-4-2-4444-4422-2-222-20000-44-4000022-2-2-2-222000000002-200000000000000000000000000000000000000
χ644444-4-4-2-44-4-4-4422-2-222-200004-44000022-2-222-2-200000000-2200000000000000000000000000000000000000
χ6544-4-44-4-24-400-44-2-2-2222200000004i−4i4i−4i-22-220000000000000000000000−2i2i−2i2i00000000000000000000000000
χ6644-4-44-4-24-400-44-2-2-222220000000−4i4i−4i4i-22-2200000000000000000000002i−2i2i−2i00000000000000000000000000
χ6744-4-44-4-2-44004-4-2-2-2222200000004i−4i−4i4i2-22-20000000000000000000000−2i2i2i−2i00000000000000000000000000
χ6844-4-44-4-2-44004-4-2-2-222220000000−4i4i4i−4i2-22-200000000000000000000002i−2i−2i2i00000000000000000000000000
χ6944-4-4-44-24400-4-422-22-2-224-44-40000000-222-200000000-22-220000000000000000000000000000000000000000
χ7044-4-4-44-24400-4-422-22-2-22-44-440000000-222-2000000002-22-20000000000000000000000000000000000000000
χ7144-4-4-44-2-4-4004422-22-2-224-4-4400000002-2-2200000000-222-20000000000000000000000000000000000000000
χ7244-4-4-44-2-4-4004422-22-2-22-444-400000002-2-22000000002-2-220000000000000000000000000000000000000000
χ734-4-44004004-40000-4-40040000000000000004-4002-22-20000002-22-22-22-2000000000000000000000000000000
χ744-4-44004004-40000-4-40040000000000000004-400-22-22000000-22-22-22-22000000000000000000000000000000
χ754-4-4400400-440000-4-4004000000000000000-44002-2-220000002-22-2-22-22000000000000000000000000000000
χ764-4-4400400-440000-4-4004000000000000000-4400-222-2000000-22-222-22-2000000000000000000000000000000
χ774-4-4400-2004-400−2i32i322−2i32i3-2000000000000000-22−2i32i32-22-2000000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000000
χ784-4-4400-2004-400−2i32i322−2i32i3-2000000000000000-22−2i32i3-22-220000001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000000
χ794-4-4400-2004-4002i3−2i3222i3−2i3-2000000000000000-222i3−2i32-22-2000000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000000
χ804-4-4400-2004-4002i3−2i3222i3−2i3-2000000000000000-222i3−2i3-22-220000001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000000
χ814-4-4400-200-4400−2i32i322−2i32i3-20000000000000002-22i3−2i32-2-22000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3000000000000000000000000000000
χ824-4-4400-200-4400−2i32i322−2i32i3-20000000000000002-22i3−2i3-222-20000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000
χ834-4-4400-200-44002i3−2i3222i3−2i3-20000000000000002-2−2i32i32-2-22000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3000000000000000000000000000000
χ844-4-4400-200-44002i3−2i3222i3−2i3-20000000000000002-2−2i32i3-222-20000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000
χ858-88-800800000000-8800-80000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-4000000−4i34i34-44i3−4i340000000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-40000004i3−4i34-4−4i34i340000000000000000000000000000000000000000000000000000000000000000000

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