Finite Group Databasebeta

← Group #10826337

Character table — Group #10826337

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order122222223444466666662222226666121212122244466666666888812122424242424242424224444412121212222244488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-1-1
χ41111111111111111111111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111
χ5111111111111111111111111-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-111-1
χ6111111111111111111111111-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111111-1-11
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111-1-111-1-1-1-1-111-1-11
χ8111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-111111-1-111-1
χ911111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1111-1-1-1-1-1-11
χ1011111111111111111111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1111111-1
χ1111111111111111111111-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-11-1-11111-1
χ1211111111111111111111-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111-11111-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-11111-1-11-1-1-1-1111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1111-1-1-1-1-1-1-111-1-1111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111111-1-111111-1-111-1-1-1
χ17222222222-2-2-2-222222220000222222-2-2-2-200-200000000000000-2-20000000022-2-222000000000-20000000
χ18222222222-2-2-2-222222220000222222-2-2-2-200-200000000000000-2-200000000-2-222-2-200000000020000000
χ19222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-200200000000000000220000000022-2-2-2-200000000020000000
χ20222222222-2-2-2-222222220000-2-2-2-2-2-2-2-2-2-2002000000000000002200000000-2-22222000000000-20000000
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
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-222-1-1-1-11111-2-22211-1-1-1-11111000000-211-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-21111-1-1-1-1-2-2-2-2-2-1-1-1-1111122-2-2111111-1-1-1-10000002-1-111000000000000
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
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-22-2-2111111112222-1-1-1-1-1-1-1-1-1-1000000-21111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2221111-1-1-1-122-2-2111111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-122-2-2-21111-1-1-1-1-2-22211-1-1-1-111110000002-1-111000000000000
χ2922-22-2-22-22-22-222-2-2-2-22222-2-2000000-2-2220002-222-2-20000002-20022-2-200000000000002-2000000000000
χ3022-22-2-22-22-22-222-2-2-2-22222-2-2000000-2-222000-2222-2-2000000-2200-2-2220000000000000-22000000000000
χ3122-22-2-22-22-22-222-2-2-2-222-2-222000000-2-2220002-2-2-222000000-2200-2-22200000000000002-2000000000000
χ3222-22-2-22-22-22-222-2-2-2-222-2-222000000-2-222000-22-2-2220000002-20022-2-20000000000000-22000000000000
χ3322-22-2-22-2-1-22-22-11111-1-122-2-200−i3−i3i3i311-1-10002-2-1-111−i3−i3i3i3002-2−i3i3-1-111−i3−i3i3i30000000−i3i3-11000000000000
χ3422-22-2-22-2-1-22-22-11111-1-122-2-200−i3−i3i3i311-1-1000-22-1-111−i3−i3i3i300-22−i3i311-1-1i3i3−i3−i30000000i3−i31-1000000000000
χ3522-22-2-22-2-1-22-22-11111-1-122-2-200i3i3−i3−i311-1-10002-2-1-111i3i3−i3−i3002-2i3−i3-1-111i3i3−i3−i30000000i3−i3-11000000000000
χ3622-22-2-22-2-1-22-22-11111-1-122-2-200i3i3−i3−i311-1-1000-22-1-111i3i3−i3−i300-22i3−i311-1-1−i3−i3i3i30000000−i3i31-1000000000000
χ3722-22-2-22-2-1-22-22-11111-1-1-2-22200−i3−i3i3i311-1-10002-211-1-1i3i3−i3−i300-22−i3i311-1-1i3i3−i3−i30000000−i3i3-11000000000000
χ3822-22-2-22-2-1-22-22-11111-1-1-2-22200−i3−i3i3i311-1-1000-2211-1-1i3i3−i3−i3002-2−i3i3-1-111−i3−i3i3i30000000i3−i31-1000000000000
χ3922-22-2-22-2-1-22-22-11111-1-1-2-22200i3i3−i3−i311-1-10002-211-1-1−i3−i3i3i300-22i3−i311-1-1−i3−i3i3i30000000i3−i3-11000000000000
χ4022-22-2-22-2-1-22-22-11111-1-1-2-22200i3i3−i3−i311-1-1000-2211-1-1−i3−i3i3i3002-2i3−i3-1-111i3i3−i3−i30000000−i3i31-1000000000000
χ412-22-2-222-22-2-222-222-2-2-222-22-20000002-22-2000002-22-200000000000000000000000000000002-2000002-20
χ422-22-2-222-22-2-222-222-2-2-222-22-20000002-22-2000002-22-20000000000000000000000000000000-2200000-220
χ432-22-2-222-22-2-222-222-2-2-22-22-220000002-22-200000-22-2200000000000000000000000000000002-200000-220
χ442-22-2-222-22-2-222-222-2-2-22-22-220000002-22-200000-22-220000000000000000000000000000000-22000002-20
χ452-2-2-22-22222-2-22-2-2-222-222-2-22000000-222-2000002-2-220000000000000000002-22-200000002-20000000000
χ462-2-2-22-22222-2-22-2-2-222-222-2-22000000-222-2000002-2-22000000000000000000-22-220000000-220000000000
χ472-2-2-22-22222-2-22-2-2-222-22-222-2000000-222-200000-222-20000000000000000002-22-20000000-220000000000
χ482-2-2-22-22222-2-22-2-2-222-22-222-2000000-222-200000-222-2000000000000000000-22-2200000002-20000000000
χ492-2-2-22-2222-222-2-2-2-222-2200000000002-2-222-200000002-22-2000000000000002-2-220000000000002-200000
χ502-2-2-22-2222-222-2-2-2-222-2200000000002-2-222-200000002-22-200000000000000-222-2000000000000-2200000
χ512-2-2-22-2222-222-2-2-2-222-2200000000002-2-22-220000000-22-22000000000000002-2-22000000000000-2200000
χ522-2-2-22-2222-222-2-2-2-222-2200000000002-2-22-220000000-22-2200000000000000-222-20000000000002-200000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-2-2-2-2222200-400000000000000220000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-42222222200400000000000000-2-20000000000000000000000000000000
χ55444-44-4-4-44000044-44-4-4-4000000000000000000000000000−2i22i200000000−2i22i2−2i22i200000000000000000000000
χ56444-44-4-4-44000044-44-4-4-40000000000000000000000000002i2−2i2000000002i2−2i22i2−2i200000000000000000000000
χ57444-44-4-4-4-20000-2-22-2222000000−2i32i3−2i32i300000000000000000−2i22i200006−66−6i2−i2i2−i200000000000000000000000
χ58444-44-4-4-4-20000-2-22-2222000000−2i32i3−2i32i3000000000000000002i2−2i20000−66−66−i2i2−i2i200000000000000000000000
χ59444-44-4-4-4-20000-2-22-22220000002i3−2i32i3−2i300000000000000000−2i22i20000−66−66i2−i2i2−i200000000000000000000000
χ60444-44-4-4-4-20000-2-22-22220000002i3−2i32i3−2i3000000000000000002i2−2i200006−66−6−i2i2−i2i200000000000000000000000
χ6144-44-4-44-444-44-44-4-4-4-444000000000044-4-400000000000000000000000000000000000000000000000000
χ6244-44-4-44-4-24-44-4-22222-2-2000000−2i3−2i32i32i3-2-222000000000000000002i3−2i30000000000000000000000000000000
χ6344-44-4-44-4-24-44-4-22222-2-20000002i32i3−2i3−2i3-2-22200000000000000000−2i32i30000000000000000000000000000000
χ6444-4-4-44-44400004-44-44-4-400004-44-4-44000000000000000000000000000000000000000000000000000000
χ6544-4-4-44-44400004-44-44-4-40000-44-444-4000000000000000000000000000000000000000000000000000000
χ6644-4-4-44-44-20000-22-22-22200004-4-222-2000000000000000000000006−6−66−666−600000000000000000000000
χ6744-4-4-44-44-20000-22-22-22200004-4-222-200000000000000000000000−666−66−6−6600000000000000000000000
χ6844-4-4-44-44-20000-22-22-2220000-442-2-22000000000000000000000006−6−666−6−6600000000000000000000000
χ6944-4-4-44-44-20000-22-22-2220000-442-2-2200000000000000000000000−666−6−666−600000000000000000000000
χ704-444-4-4-4440000-44-4-444-40000000000000000000000000000000000000000000004-400000000000000000
χ714-444-4-4-4440000-44-4-444-4000000000000000000000000000000000000000000000-4400000000000000000
χ724-44-4-444-4444-4-4-444-4-4-440000000000-44-4400000000000000000000000000000000000000000000000000
χ734-44-4-444-4-244-4-42-2-2222-200000000002-22-2000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ744-44-4-444-4-244-4-42-2-2222-200000000002-22-20000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ754-44-4-444-4-2-4-4442-2-2222-24-44-4000000-22-2200000-22-2200000000000000000000000000000000000000000
χ764-44-4-444-4-2-4-4442-2-2222-2-44-44000000-22-22000002-22-200000000000000000000000000000000000000000
χ774-4-4444-4-440000-4-444-44-40000000000000000000000000000000000000000000000000000000000022−22000
χ784-4-4444-4-440000-4-444-44-400000000000000000000000000000000000000000000000000000000000−2222000
χ794-4-4-44-444-24-4-44222-2-22-24-4-440000002-2-2200000-222-200000000000000000000000000000000000000000
χ804-4-4-44-444-24-4-44222-2-22-2-444-40000002-2-22000002-2-2200000000000000000000000000000000000000000
χ814-4-4-44-444-2-444-4222-2-22-20000000000-222-24-40000000-22-220000000000000000000000000000000000000
χ824-4-4-44-444-2-444-4222-2-22-20000000000-222-2-4400000002-22-20000000000000000000000000000000000000
χ838-888-8-8-88-400004-444-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8888-8-8-4000044-4-44-440000000000000000000000000000000000000000000000000000000000000000

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