Finite Group Databasebeta

← Group #10714564

Character table — Group #10714564

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122222344446666666888844448888881212121212121212121212122424242424242424242424242424242422226666666616161616161616164488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222222222222-2-2-2-22222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ10222222222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ11222222-12222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ12222222-12222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ13222222-12222-1-1-1-1-1-1-12222-2-2-2-222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ14222222-12222-1-1-1-1-1-1-12222-2-2-2-222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ15222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3−i3i3i3−i3−i3i3i3000000000000
χ16222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3i3−i3−i3i3i3−i3−i3000000000000
χ17222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000−i3−i3i3i3i3i3−i3−i3000000000000
χ18222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000i3i3−i3−i3−i3−i3i3i3000000000000
χ192222-2-222-22-222-2-22-2-222220000-2-200002-2000000002-22222-2-2-2-200000000000000000000000000002-200
χ202222-2-222-22-222-2-22-2-222220000-2-200002-2000000002-22222-2-2-2-20000000000000000000000000000-2200
χ212222-2-222-22-222-2-22-2-2-2-2-2-200002200002-2000000002-2-2-2-2-222220000000000000000000000000000002i−2i
χ222222-2-222-22-222-2-22-2-2-2-2-2-200002200002-2000000002-2-2-2-2-22222000000000000000000000000000000−2i2i
χ232222-2-22-22-2222-2-22-2-2000000000022-2-2-2200000000-22000000002222-2-2-2-200000000000022−2−222−2−20000
χ242222-2-22-22-2222-2-22-2-2000000000022-2-2-2200000000-22000000002222-2-2-2-2000000000000−2−222−2−2220000
χ252222-2-22-22-2222-2-22-2-20000000000-2-222-2200000000-2200000000-2-2-2-2222200000000000022−2−2−2−2220000
χ262222-2-22-22-2222-2-22-2-20000000000-2-222-2200000000-2200000000-2-2-2-22222000000000000−2−22222−2−20000
χ2722-2-22-22-222-2-2-2222-2-222-2-200002-20000-22000000002-222-2-222-2-20000000000000000000000002i−2i2i−2i0000
χ2822-2-22-22-222-2-2-2222-2-222-2-200002-20000-22000000002-222-2-222-2-2000000000000000000000000−2i2i−2i2i0000
χ2922-2-22-22-222-2-2-2222-2-2-2-2220000-220000-22000000002-2-2-222-2-222000000000000000000002i−2i2i−2i00000000
χ3022-2-22-22-222-2-2-2222-2-2-2-2220000-220000-22000000002-2-2-222-2-22200000000000000000000−2i2i−2i2i00000000
χ3122-2-2-22222-2-2-2-2-2-2222000022-2-2000000222222-2-2-2-2-2-20000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ3222-2-2-22222-2-2-2-2-2-2222000022-2-2000000222222-2-2-2-2-2-20000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ3322-2-2-22222-2-2-2-2-2-22220000-2-22200000022-2-2-2-22222-2-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ3422-2-2-22222-2-2-2-2-2-22220000-2-22200000022-2-2-2-22222-2-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ3522-2-2-222-2-222-2-2-2-222222-2-20000-220000-2-2000000002222-2-2-2-22200000000002-200002-22-2000000000000
χ3622-2-2-222-2-222-2-2-2-222222-2-20000-220000-2-2000000002222-2-2-2-2220000000000-220000-22-22000000000000
χ3722-2-2-222-2-222-2-2-2-2222-2-22200002-20000-2-20000000022-2-22222-2-2000000002-2002-22-20000000000000000
χ3822-2-2-222-2-222-2-2-2-2222-2-22200002-20000-2-20000000022-2-22222-2-200000000-2200-22-220000000000000000
χ3922-2-2-22-1-2-2221111-1-1-122-2-20000-22000011−i3−i3i3i3−i3−i3i3i3-1-1-1-11111-1-1−i3−i3i3i3−i3−i3i3i3002-2−i3i3i3−i3-11-11000000000000
χ4022-2-2-22-1-2-2221111-1-1-122-2-20000-22000011−i3−i3i3i3−i3−i3i3i3-1-1-1-11111-1-1−i3−i3i3i3−i3−i3i3i300-22i3−i3−i3i31-11-1000000000000
χ4122-2-2-22-1-2-2221111-1-1-122-2-20000-22000011i3i3−i3−i3i3i3−i3−i3-1-1-1-11111-1-1i3i3−i3−i3i3i3−i3−i3002-2i3−i3−i3i3-11-11000000000000
χ4222-2-2-22-1-2-2221111-1-1-122-2-20000-22000011i3i3−i3−i3i3i3−i3−i3-1-1-1-11111-1-1i3i3−i3−i3i3i3−i3−i300-22−i3i3i3−i31-11-1000000000000
χ4322-2-2-22-1-2-2221111-1-1-1-2-22200002-2000011−i3−i3i3i3−i3−i3i3i3-1-111-1-1-1-111i3i3−i3−i3i3i3−i3−i32-200-11-11−i3i3i3−i3000000000000
χ4422-2-2-22-1-2-2221111-1-1-1-2-22200002-2000011−i3−i3i3i3−i3−i3i3i3-1-111-1-1-1-111i3i3−i3−i3i3i3−i3−i3-22001-11-1i3−i3−i3i3000000000000
χ4522-2-2-22-1-2-2221111-1-1-1-2-22200002-2000011i3i3−i3−i3i3i3−i3−i3-1-111-1-1-1-111−i3−i3i3i3−i3−i3i3i32-200-11-11i3−i3−i3i3000000000000
χ4622-2-2-22-1-2-2221111-1-1-1-2-22200002-2000011i3i3−i3−i3i3i3−i3−i3-1-111-1-1-1-111−i3−i3i3i3−i3−i3i3i3-22001-11-1−i3i3i3−i3000000000000
χ474444444-4-4-4-4444444400000000000000-4-400000000-4-40000000000000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-2-2-2-2-20000000000000022−2i3−2i32i32i32i32i3−2i3−2i3220000000000000000000000000000000000000000
χ49444444-2-4-4-4-4-2-2-2-2-2-2-200000000000000222i32i3−2i3−2i3−2i3−2i32i32i3220000000000000000000000000000000000000000
χ504444-4-4-24-44-4-2-222-22244440000-4-40000-2200000000-22-2-2-2-2222200000000000000000000000000000000
χ514444-4-4-24-44-4-2-222-222-4-4-4-40000440000-2200000000-222222-2-2-2-200000000000000000000000000000000
χ524444-4-4-2-44-44-2-222-222000000000044-4-42-2000000002-200000000-2-2-2-22222000000000000000000000000
χ534444-4-4-2-44-44-2-222-2220000000000-4-4442-2000000002-2000000002222-2-2-2-2000000000000000000000000
χ5444-4-44-444-4-44-4-4444-4-4000000000000004-400000000-440000000000000000000000000000000000000000
χ5544-4-44-4-24-4-4422-2-2-22200000000000000-22000000002-200000000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000
χ5644-4-44-4-24-4-4422-2-2-22200000000000000-22000000002-2000000002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000
χ5744-4-44-4-2-444-422-2-2-22244-4-400004-400002-200000000-22-2-222-2-22200000000000000000000000000000000
χ5844-4-44-4-2-444-422-2-2-222-4-4440000-4400002-200000000-2222-2-222-2-200000000000000000000000000000000
χ5944-4-4-44-244-4-42222-2-2-2000044-4-4000000-2-2-2-2-2-22222220000000000000000000000000000000000000000
χ6044-4-4-44-244-4-42222-2-2-20000-4-444000000-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ614-44-400400004-400-40022−2222−222-22-2000022−22002-22-22-22-20022−2222−220000000022−2222−22000000000000000000000000
χ624-44-400400004-400-40022−2222−22-22-220000−222200-22-22-22-220022−2222−2200000000−2222−2222000000000000000000000000
χ634-44-400400004-400-400−2222−22222-22-20000−2222002-22-22-22-200−2222−222200000000−2222−2222000000000000000000000000
χ644-44-400400004-400-400−2222−2222-22-22000022−2200-22-22-22-2200−2222−22220000000022−2222−22000000000000000000000000
χ654-44-400-20000-22−2i32i32−2i32i322−2222−222-22-2000022−2200−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i300−22−22i6−i6i6−i6i6−i6i6−i6−22−22000000000000000000000000
χ664-44-400-20000-22−2i32i32−2i32i322−2222−22-22-220000−2222001+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i300−22−22i6−i6i6−i6−i6i6−i6i62−22−2000000000000000000000000
χ674-44-400-20000-22−2i32i32−2i32i3−2222−22222-22-20000−222200−1−i31+i3−1+i31−i3−1+i31−i3−1−i31+i3002−22−2−i6i6−i6i6−i6i6−i6i62−22−2000000000000000000000000
χ684-44-400-20000-22−2i32i32−2i32i3−2222−2222-22-22000022−22001+i3−1−i31−i3−1+i31−i3−1+i31+i3−1−i3002−22−2−i6i6−i6i6i6−i6i6−i6−22−22000000000000000000000000
χ694-44-400-20000-222i3−2i322i3−2i322−2222−222-22-2000022−2200−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i300−22−22−i6i6−i6i6−i6i6−i6i6−22−22000000000000000000000000
χ704-44-400-20000-222i3−2i322i3−2i322−2222−22-22-220000−2222001−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i300−22−22−i6i6−i6i6i6−i6i6−i62−22−2000000000000000000000000
χ714-44-400-20000-222i3−2i322i3−2i3−2222−22222-22-20000−222200−1+i31−i3−1−i31+i3−1−i31+i3−1+i31−i3002−22−2i6−i6i6−i6i6−i6i6−i62−22−2000000000000000000000000
χ724-44-400-20000-222i3−2i322i3−2i3−2222−2222-22-22000022−22001−i3−1+i31+i3−1−i31+i3−1−i31−i3−1+i3002−22−2i6−i6i6−i6−i6i6−i6i6−22−22000000000000000000000000
χ734-4-440040000-4400-40022−22−22222-2-220022−2200002-22-2-22-220022−22−22220000−222222−220000000000000000000000000000
χ744-4-440040000-4400-40022−22−2222-222-200−22220000-22-222-22-20022−22−2222000022−22−22220000000000000000000000000000
χ754-4-440040000-4400-400−222222−222-2-2200−222200002-22-2-22-2200−222222−22000022−22−22220000000000000000000000000000
χ764-4-440040000-4400-400−222222−22-222-20022−220000-22-222-22-200−222222−220000−222222−220000000000000000000000000000
χ774-4-4400-200002-2−2i32i322i3−2i322−22−22222-2-220022−220000−1+i31−i3−1−i31+i31+i3−1−i31−i3−1+i300−222−2i6−i6−i6i62−2−22i6−i6−i6i6000000000000000000000000
χ784-4-4400-200002-2−2i32i322i3−2i322−22−2222-222-200−222200001−i3−1+i31+i3−1−i3−1−i31+i3−1+i31−i300−222−2i6−i6−i6i6−222−2−i6i6i6−i6000000000000000000000000
χ794-4-4400-200002-2−2i32i322i3−2i3−222222−222-2-2200−22220000−1+i31−i3−1−i31+i31+i3−1−i31−i3−1+i3002−2−22−i6i6i6−i6−222−2−i6i6i6−i6000000000000000000000000
χ804-4-4400-200002-2−2i32i322i3−2i3−222222−22-222-20022−2200001−i3−1+i31+i3−1−i3−1−i31+i3−1+i31−i3002−2−22−i6i6i6−i62−2−22i6−i6−i6i6000000000000000000000000
χ814-4-4400-200002-22i3−2i32−2i32i322−22−22222-2-220022−220000−1−i31+i3−1+i31−i31−i3−1+i31+i3−1−i300−222−2−i6i6i6−i62−2−22−i6i6i6−i6000000000000000000000000
χ824-4-4400-200002-22i3−2i32−2i32i322−22−2222-222-200−222200001+i3−1−i31−i3−1+i3−1+i31−i3−1−i31+i300−222−2−i6i6i6−i6−222−2i6−i6−i6i6000000000000000000000000
χ834-4-4400-200002-22i3−2i32−2i32i3−222222−222-2-2200−22220000−1−i31+i3−1+i31−i31−i3−1+i31+i3−1−i3002−2−22i6−i6−i6i6−222−2i6−i6−i6i6000000000000000000000000
χ844-4-4400-200002-22i3−2i32−2i32i3−222222−22-222-20022−2200001+i3−1−i31−i3−1+i3−1+i31−i3−1−i31+i3002−2−22i6−i6−i6i62−2−22−i6i6i6−i6000000000000000000000000

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