Finite Group Databasebeta

← Group #10826329

Character table — Group #10826329

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order1222222234444666666622222266661212121222224666666668888121224242424242424242244444661212224444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111-1-1-1-1-1-11111-1-111-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-111-1-111-1-1-111-1-111-1
χ6111111111111111111111111-1-1-1-1-1-11111-1-111-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-1111-1-111-1-11
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111-1-11111-1-1-1-1-111-1-11
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11-1-111-1-111111-1-111-1
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-11111-1
χ1111111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-11-1-1-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1111111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-1111-1-1-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1111-1-111-1-1-111-1-1-1-1111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-11-1-111111-1-11111-1-1-1
χ17222222222-2-2-2-222222220000222222-2-2-2-20000-2000000000000-2-2000000002222-2-20000000-2000000000
χ18222222222-2-2-2-222222220000222222-2-2-2-20000-2000000000000-2-200000000-2-2-2-22200000002000000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200002000000000000220000000022-2-2-2-200000002000000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2000020000000000002200000000-2-222220000000-2000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-22-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-222-2-1-1-1-11111-2-22211-1-1-1-11111000000-2-1-111000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-2-2-1-1-1-1111122-2-2111111-1-1-1-1000000211-1-1000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-222211111111-2-2-2-2-1-1111111110000002-1-1-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-22111111112222-1-1-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12222-21111-1-1-1-122-2-2111111-1-1-1-1000000-2-1-111000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-2-21111-1-1-1-1-2-22211-1-1-1-11111000000211-1-1000000000000
χ2922-22-2-2-222-22-222-2-2-2-22222-2-2000000-2-222002-2022-2-20000002-20022-2-2000000000002-200000000000000
χ3022-22-2-2-222-22-222-2-2-2-22222-2-2000000-2-22200-22022-2-2000000-2200-2-22200000000000-2200000000000000
χ3122-22-2-2-222-22-222-2-2-2-222-2-222000000-2-222002-20-2-222000000-2200-2-222000000000002-200000000000000
χ3222-22-2-2-222-22-222-2-2-2-222-2-222000000-2-22200-220-2-2220000002-20022-2-200000000000-2200000000000000
χ3322-22-2-2-22-1-22-22-11111-1-122-2-200−i3−i3i3i311-1-1002-20-1-111−i3−i3i3i3002-2−i3i3-1-111−i3−i3i3i30000000-11−i3i3000000000000
χ3422-22-2-2-22-1-22-22-11111-1-122-2-200−i3−i3i3i311-1-100-220-1-111−i3−i3i3i300-22−i3i311-1-1i3i3−i3−i300000001-1i3−i3000000000000
χ3522-22-2-2-22-1-22-22-11111-1-122-2-200i3i3−i3−i311-1-1002-20-1-111i3i3−i3−i3002-2i3−i3-1-111i3i3−i3−i30000000-11i3−i3000000000000
χ3622-22-2-2-22-1-22-22-11111-1-122-2-200i3i3−i3−i311-1-100-220-1-111i3i3−i3−i300-22i3−i311-1-1−i3−i3i3i300000001-1−i3i3000000000000
χ3722-22-2-2-22-1-22-22-11111-1-1-2-22200−i3−i3i3i311-1-1002-2011-1-1i3i3−i3−i300-22−i3i311-1-1i3i3−i3−i30000000-11−i3i3000000000000
χ3822-22-2-2-22-1-22-22-11111-1-1-2-22200−i3−i3i3i311-1-100-22011-1-1i3i3−i3−i3002-2−i3i3-1-111−i3−i3i3i300000001-1i3−i3000000000000
χ3922-22-2-2-22-1-22-22-11111-1-1-2-22200i3i3−i3−i311-1-1002-2011-1-1−i3−i3i3i300-22i3−i311-1-1−i3−i3i3i30000000-11i3−i3000000000000
χ4022-22-2-2-22-1-22-22-11111-1-1-2-22200i3i3−i3−i311-1-100-22011-1-1−i3−i3i3i3002-2i3−i3-1-111i3i3−i3−i300000001-1−i3i3000000000000
χ412-22-2-22-222-2-222-222-2-22-22-22-20000002-22-2000002-22-200000000000000000000000000000000002-2002-20
χ422-22-2-22-222-2-222-222-2-22-22-22-20000002-22-2000002-22-20000000000000000000000000000000000-2200-220
χ432-22-2-22-222-2-222-222-2-22-2-22-220000002-22-200000-22-2200000000000000000000000000000000002-200-220
χ442-22-2-22-222-2-222-222-2-22-2-22-220000002-22-200000-22-220000000000000000000000000000000000-22002-20
χ452-2-2-22-22222-2-22-2-2-2222-22-2-22000000-222-2000002-2-220000000000000000002-2002-2000002-20000000000
χ462-2-2-22-22222-2-22-2-2-2222-22-2-22000000-222-2000002-2-22000000000000000000-2200-2200000-220000000000
χ472-2-2-22-22222-2-22-2-2-2222-2-222-2000000-222-200000-222-20000000000000000002-2002-200000-220000000000
χ482-2-2-22-22222-2-22-2-2-2222-2-222-2000000-222-200000-222-2000000000000000000-2200-22000002-20000000000
χ492-2-2-22-2222-222-2-2-2-2222-200000000002-2-222-200000002-22-2000000000000002-200-22000000002-20000000
χ502-2-2-22-2222-222-2-2-2-2222-200000000002-2-222-200000002-22-200000000000000-22002-200000000-220000000
χ512-2-2-22-2222-222-2-2-2-2222-200000000002-2-22-220000000-22-22000000000000002-200-2200000000-220000000
χ522-2-2-22-2222-222-2-2-2-2222-200000000002-2-22-220000000-22-2200000000000000-22002-2000000002-20000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-2-2-2-222220000-4000000000000220000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-42222222200004000000000000-2-20000000000000000000000000000000
χ55444-44-4-4-44000044-44-4-4-400000000000000000000000000000000000000000000000000000000000−2i22i2000
χ56444-44-4-4-44000044-44-4-4-4000000000000000000000000000000000000000000000000000000000002i2−2i2000
χ5744-44-4-4-4444-44-44-4-4-4-444000000000044-4-400000000000000000000000000000000000000000000000000
χ5844-44-4-4-44-24-44-4-22222-2-2000000−2i3−2i32i32i3-2-222000000000000000002i3−2i30000000000000000000000000000000
χ5944-44-4-4-44-24-44-4-22222-2-20000002i32i3−2i3−2i3-2-22200000000000000000−2i32i30000000000000000000000000000000
χ6044-4-4-444-4400004-44-44-4-400000000000000000000000000000000000000000004-40000000000000000000
χ6144-4-4-444-4400004-44-44-4-40000000000000000000000000000000000000000000-440000000000000000000
χ624-444-4-44-440000-44-4-44-4400004-44-44-4000000000000000000000000000000000000000000000000000000
χ634-444-4-44-440000-44-4-44-440000-44-44-44000000000000000000000000000000000000000000000000000000
χ644-444-4-44-4-200002-222-22-200004-4-22-2200000000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ654-444-4-44-4-200002-222-22-200004-4-22-2200000000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ664-444-4-44-4-200002-222-22-20000-442-22-200000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ674-444-4-44-4-200002-222-22-20000-442-22-200000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ684-44-4-44-44444-4-4-444-4-44-40000000000-44-4400000000000000000000000000000000000000000000000000
χ694-44-4-44-44-244-4-42-2-222-2200000000002-22-2000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ704-44-4-44-44-244-4-42-2-222-2200000000002-22-20000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ714-44-4-44-44-2-4-4442-2-222-224-44-4000000-22-2200000-22-2200000000000000000000000000000000000000000
χ724-44-4-44-44-2-4-4442-2-222-22-44-44000000-22-22000002-22-200000000000000000000000000000000000000000
χ734-4-4444-4-440000-4-444-4-4400000000000000000000000000022−220000000022−22−222200000000000000000000000
χ744-4-4444-4-440000-4-444-4-44000000000000000000000000000−222200000000−222222−2200000000000000000000000
χ754-4-4444-4-4-2000022-2-222-2000000−2i32i32i3−2i30000000000000000022−220000−i6i6i6−i6−222−200000000000000000000000
χ764-4-4444-4-4-2000022-2-222-2000000−2i32i32i3−2i300000000000000000−22220000i6−i6−i6i62−2−2200000000000000000000000
χ774-4-4444-4-4-2000022-2-222-20000002i3−2i3−2i32i30000000000000000022−220000i6−i6−i6i6−222−200000000000000000000000
χ784-4-4444-4-4-2000022-2-222-20000002i3−2i3−2i32i300000000000000000−22220000−i6i6i6−i62−2−2200000000000000000000000
χ794-4-4-44-444-24-4-44222-2-2-224-4-440000002-2-2200000-222-200000000000000000000000000000000000000000
χ804-4-4-44-444-24-4-44222-2-2-22-444-40000002-2-22000002-2-2200000000000000000000000000000000000000000
χ814-4-4-44-444-2-444-4222-2-2-220000000000-222-24-40000000-22-220000000000000000000000000000000000000
χ824-4-4-44-444-2-444-4222-2-2-220000000000-222-2-4400000002-22-20000000000000000000000000000000000000
χ83888-88-8-8-8-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-888-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000

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