Finite Group Databasebeta

← Group #10858125

Character table — Group #10858125

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order1222222234444666666622444444121212121212121244668888121212121212121224242424242424244444441212121244444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-11111
χ61111111111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1
χ71111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-111-1-1-1-11111
χ911111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-11-111-1-1111-1-1-111-1-111-1-1
χ1011111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-111-1-1-1-1-1111-1-111-1-111
χ1111111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-11-1-111111-1-1-1-1-111-1-111
χ1211111111111111111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-11-1-111-1-1-111111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-11-1-1111-1-1-111-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-11-1-111-1111-1-111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-111-1-11-1-1-11111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-111-1-1-1111-1-1-1-11111-1-1
χ17222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-2-200220000000000000000000022-2-2000000-20020000000000
χ18222222222-2-2-2-22222222220000-2-2-2-2-2-2-2-2-2-2002200000000000000000000-2-222000000200-20000000000
χ19222222222-2-2-2-22222222-2-2000022-2-22222-2-200-2-2000000000000000000002222000000-200-20000000000
χ20222222222-2-2-2-22222222-2-2000022-2-22222-2-200-2-200000000000000000000-2-2-2-200000020020000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-2-2-1-1222211111111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-2-2-1-1-2-2-2-21111111111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-11111-1-1-2-21122-2-21111-1-1-1-1-1-1-1-1111100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-11111-1-1-2-211-2-2221111-1-1-1-11111-1-1-1-10000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-1221122-2-2-1-1-1-11111-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-12211-2-222-1-1-1-111111111-1-1-1-100002-2-1-11100000000000000
χ2922-2-22-22-2222-2-222-22-2-2-22-200002-22222-2-2-2-2002-200000000000000000000000000000002-202-200000000
χ3022-2-22-22-2222-2-222-22-2-2-22-200002-22222-2-2-2-2002-20000000000000000000000000000000-220-2200000000
χ3122-2-22-22-2222-2-222-22-2-2-2-220000-2222-2-222-2-200-2200000000000000000000000000000002-20-2200000000
χ3222-2-22-22-2222-2-222-22-2-2-2-220000-2222-2-222-2-200-220000000000000000000000000000000-2202-200000000
χ3322-2-22-22-22-2-22222-22-2-2-22-22i2i−2i−2i-22-2-2-2-222222i−2i2-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ3422-2-22-22-22-2-22222-22-2-2-22-2−2i−2i2i2i-22-2-2-2-22222−2i2i2-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3522-2-22-22-22-2-22222-22-2-2-2-222i2i−2i−2i2-2-2-222-2-222−2i2i-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ3622-2-22-22-22-2-22222-22-2-2-2-22−2i−2i2i2i2-2-2-222-2-2222i−2i-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ3722-2-22-22-2-1-2-222-1-11-11112-22i2i−2i−2i-221111-1-1-1-12i−2i-110000−i−iii−i−iii−i3−i3i3i3−i3−i3i3i30000003−33−300000000000000
χ3822-2-22-22-2-1-2-222-1-11-11112-22i2i−2i−2i-221111-1-1-1-12i−2i-110000−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3000000−33−3300000000000000
χ3922-2-22-22-2-1-2-222-1-11-11112-2−2i−2i2i2i-221111-1-1-1-1−2i2i-110000ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3000000−33−3300000000000000
χ4022-2-22-22-2-1-2-222-1-11-11112-2−2i−2i2i2i-221111-1-1-1-1−2i2i-110000ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i30000003−33−300000000000000
χ4122-2-22-22-2-1-2-222-1-11-1111-222i2i−2i−2i2-211-1-111-1-1−2i2i1-10000ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000003−3−3300000000000000
χ4222-2-22-22-2-1-2-222-1-11-1111-222i2i−2i−2i2-211-1-111-1-1−2i2i1-10000ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000−333−300000000000000
χ4322-2-22-22-2-1-2-222-1-11-1111-22−2i−2i2i2i2-211-1-111-1-12i−2i1-10000−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000−333−300000000000000
χ4422-2-22-22-2-1-2-222-1-11-1111-22−2i−2i2i2i2-211-1-111-1-12i−2i1-10000−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000003−3−3300000000000000
χ452-222-2-22-222-2-22-2-2222-2-2002i−2i2i−2i002-200002-20000000000002i−2i2i−2i000000000000000000000000002i−2i002-2
χ462-222-2-22-222-2-22-2-2222-2-2002i−2i2i−2i002-200002-20000000000002i−2i2i−2i00000000000000000000000000−2i2i00-22
χ472-222-2-22-222-2-22-2-2222-2-200−2i2i−2i2i002-200002-2000000000000−2i2i−2i2i000000000000000000000000002i−2i00-22
χ482-222-2-22-222-2-22-2-2222-2-200−2i2i−2i2i002-200002-2000000000000−2i2i−2i2i00000000000000000000000000−2i2i002-2
χ492-2-2-2-22222-22-22-2-2-22-222002-2-2200-2200002-20000000000002-2-220000000000000000000000002-2002-200
χ502-2-2-2-22222-22-22-2-2-22-222002-2-2200-2200002-20000000000002-2-22000000000000000000000000-2200-2200
χ512-2-2-2-22222-22-22-2-2-22-22200-222-200-2200002-2000000000000-222-20000000000000000000000002-200-2200
χ522-2-2-2-22222-22-22-2-2-22-22200-222-200-2200002-2000000000000-222-2000000000000000000000000-22002-200
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-4-42222222200-2-200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-400004422-2-2-2-222002200000000000000000000000000000000000000000000
χ55444-4-44-4-4400004-44-4-4-44000000000000000000000022−2200000000000022−2222−22000000000000000000000000
χ56444-4-44-4-4400004-44-4-4-440000000000000000000000−2222000000000000−2222−2222000000000000000000000000
χ57444-4-44-4-4-20000-22-2222-2000000000023−2323−230000000022−22000000006−66−6−22−22000000000000000000000000
χ58444-4-44-4-4-20000-22-2222-2000000000023−2323−2300000000−222200000000−66−662−22−2000000000000000000000000
χ59444-4-44-4-4-20000-22-2222-20000000000−2323−23230000000022−2200000000−66−66−22−22000000000000000000000000
χ60444-4-44-4-4-20000-22-2222-20000000000−2323−232300000000−2222000000006−66−62−22−2000000000000000000000000
χ6144-44-4-4-44400004-4-4-444-400000000000000000000−2i22i20000000000−2i22i22i2−2i20000000000000000000000000000
χ6244-44-4-4-44400004-4-4-444-4000000000000000000002i2−2i200000000002i2−2i2−2i22i20000000000000000000000000000
χ6344-44-4-4-44-20000-2222-2-22000000000023−23−2323000000−2i22i20000000000i2−i2−i2i2−i6i6i6−i6000000000000000000000000
χ6444-44-4-4-44-20000-2222-2-22000000000023−23−23230000002i2−2i20000000000−i2i2i2−i2i6−i6−i6i6000000000000000000000000
χ6544-44-4-4-44-20000-2222-2-220000000000−232323−23000000−2i22i20000000000i2−i2−i2i2i6−i6−i6i6000000000000000000000000
χ6644-44-4-4-44-20000-2222-2-220000000000−232323−230000002i2−2i20000000000−i2i2i2−i2−i6i6i6−i6000000000000000000000000
χ6744-4-44-44-4-244-4-4-2-22-22224-400004-4-2-2-2-2222200-2200000000000000000000000000000000000000000000
χ6844-4-44-44-4-244-4-4-2-22-2222-440000-44-2-222-2-222002-200000000000000000000000000000000000000000000
χ694-444-4-44-44-444-4-4-4444-4-400000000-440000-44000000000000000000000000000000000000000000000000
χ704-444-4-44-4-24-4-4422-2-2-222004i−4i4i−4i00-220000-22000000000000−2i2i−2i2i00000000000000000000000000000000
χ714-444-4-44-4-24-4-4422-2-2-22200−4i4i−4i4i00-220000-220000000000002i−2i2i−2i00000000000000000000000000000000
χ724-444-4-44-4-2-444-422-2-2-222000000002-200002-20000000023−2323−23000000000000000000000000000000000000
χ734-444-4-44-4-2-444-422-2-2-222000000002-200002-200000000−2323−2323000000000000000000000000000000000000
χ744-44-44-4-4440000-444-4-44-400000000000000000000000000000000000000004i−4i0000000000000000000000
χ754-44-44-4-4440000-444-4-44-40000000000000000000000000000000000000000−4i4i0000000000000000000000
χ764-4-4444-4-440000-44-4-44-440000000000000000000000000000000000000000004i−4i00000000000000000000
χ774-4-4444-4-440000-44-4-44-44000000000000000000000000000000000000000000−4i4i00000000000000000000
χ784-4-4-4-444444-44-4-4-4-44-444000000004-40000-44000000000000000000000000000000000000000000000000
χ794-4-4-4-4444-24-44-4222-22-2-200000000-2200002-200000000−2i32i32i3−2i3000000000000000000000000000000000000
χ804-4-4-4-4444-24-44-4222-22-2-200000000-2200002-2000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ814-4-4-4-4444-2-44-44222-22-2-2004-4-44002-20000-22000000000000-222-200000000000000000000000000000000
χ824-4-4-4-4444-2-44-44222-22-2-200-444-4002-20000-220000000000002-2-2200000000000000000000000000000000
χ838-88-88-8-88-400004-4-444-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8888-8-8-400004-444-44-40000000000000000000000000000000000000000000000000000000000000000

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