Finite Group Databasebeta

← Group #10868236

Character table — Group #10868236

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order12222222344446666666444444441212121212121212226666888812121212121224242424242424244444441212121224444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ5111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11-1-1-111-1-1-111111-1-111-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-1-111111-1-1-1-1-111-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1111-1-1-1-1-11-1-11111-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1111-1-1111-111-1-1-1-111-1-1
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-11111
χ1011111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1
χ1111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1-111-1-1-1-1
χ1211111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1111-1-1-1111-1-1-1-11111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1111-1-11-1-1-11111-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-111-111111-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1111-1-1-1-1-1111111-1-1
χ17222222222-2-2-2-22222222000022-2-2-2-22222-2-20000000000-2-20000000000002222000000-200-20000000000
χ18222222222-2-2-2-22222222000022-2-2-2-22222-2-20000000000-2-2000000000000-2-2-2-200000020020000000000
χ19222222222-2-2-2-222222220000-2-222-2-2-2-2-2-2-2-200000000002200000000000022-2-2000000200-20000000000
χ20222222222-2-2-2-222222220000-2-222-2-2-2-2-2-2-2-2000000000022000000000000-2-222000000-20020000000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-11111-1-1-2-2111122-2-211-1-1-1-1-1-1-1-1111100002-211-1-100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-11111-1-1-2-21111-2-22211-1-1-1-11111-1-1-1-10000-22-1-11100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-211112222-1-11111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-2-21111-2-2-2-2-1-1111111111111000022-1-1-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-122-1-1-1-122-2-2111111-1-1-1-111110000-22-1-11100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-122-1-1-1-1-2-2221111111111-1-1-1-100002-211-1-100000000000000
χ2922-22-2-2-2222-2-222-2-22-22-200002i−2i2i−2i2-22i2i−2i−2i2-200000000002i−2i000000000000000000000002i−2i0002-2000000
χ3022-22-2-2-2222-2-222-2-22-22-200002i−2i2i−2i2-22i2i−2i−2i2-200000000002i−2i00000000000000000000000−2i2i000-22000000
χ3122-22-2-2-2222-2-222-2-22-22-20000−2i2i−2i2i2-2−2i−2i2i2i2-20000000000−2i2i000000000000000000000002i−2i000-22000000
χ3222-22-2-2-2222-2-222-2-22-22-20000−2i2i−2i2i2-2−2i−2i2i2i2-20000000000−2i2i00000000000000000000000−2i2i0002-2000000
χ3322-22-2-2-222-222-22-2-22-22-22i2i−2i−2i2i−2i−2i2i-222i2i−2i−2i-222-222-2-20000−2i2i2i2i−2i−2i00000000000000000000000000000000
χ3422-22-2-2-222-222-22-2-22-22-22i2i−2i−2i−2i2i2i−2i-22−2i−2i2i2i-22-22-2-22200002i−2i2i2i−2i−2i00000000000000000000000000000000
χ3522-22-2-2-222-222-22-2-22-22-2−2i−2i2i2i2i−2i−2i2i-222i2i−2i−2i-22-22-2-2220000−2i2i−2i−2i2i2i00000000000000000000000000000000
χ3622-22-2-2-222-222-22-2-22-22-2−2i−2i2i2i−2i2i2i−2i-22−2i−2i2i2i-222-222-2-200002i−2i−2i−2i2i2i00000000000000000000000000000000
χ3722-22-2-2-22-1-222-2-111-11-112i2i−2i−2i2i−2i−2i2i1-1−i−iii1-12-2-1-1110000i−i−i−iii−i3−i3i3i333−3−3000000−i3i33−300000000000000
χ3822-22-2-2-22-1-222-2-111-11-112i2i−2i−2i2i−2i−2i2i1-1−i−iii1-12-2-1-1110000i−i−i−iiii3i3−i3−i3−3−333000000i3−i3−3300000000000000
χ3922-22-2-2-22-1-222-2-111-11-112i2i−2i−2i−2i2i2i−2i1-1ii−i−i1-1-2211-1-10000−ii−i−iii−i3−i3i3i3−3−333000000i3−i33−300000000000000
χ4022-22-2-2-22-1-222-2-111-11-112i2i−2i−2i−2i2i2i−2i1-1ii−i−i1-1-2211-1-10000−ii−i−iiii3i3−i3−i333−3−3000000−i3i3−3300000000000000
χ4122-22-2-2-22-1-222-2-111-11-11−2i−2i2i2i2i−2i−2i2i1-1−i−iii1-1-2211-1-10000i−iii−i−i−i3−i3i3i333−3−3000000i3−i3−3300000000000000
χ4222-22-2-2-22-1-222-2-111-11-11−2i−2i2i2i2i−2i−2i2i1-1−i−iii1-1-2211-1-10000i−iii−i−ii3i3−i3−i3−3−333000000−i3i33−300000000000000
χ4322-22-2-2-22-1-222-2-111-11-11−2i−2i2i2i−2i2i2i−2i1-1ii−i−i1-12-2-1-1110000−iiii−i−i−i3−i3i3i3−3−333000000−i3i3−3300000000000000
χ4422-22-2-2-22-1-222-2-111-11-11−2i−2i2i2i−2i2i2i−2i1-1ii−i−i1-12-2-1-1110000−iiii−i−ii3i3−i3−i333−3−3000000i3−i33−300000000000000
χ452-222-2-22-22-22-22-2222-2-2-22i−2i2i−2i0000-2-20000220000000000002i−2i2i−2i000000000000000000000000002i−2i002-2
χ462-222-2-22-22-22-22-2222-2-2-22i−2i2i−2i0000-2-20000220000000000002i−2i2i−2i00000000000000000000000000−2i2i00-22
χ472-222-2-22-22-22-22-2222-2-2-2−2i2i−2i2i0000-2-2000022000000000000−2i2i−2i2i000000000000000000000000002i−2i00-22
χ482-222-2-22-22-22-22-2222-2-2-2−2i2i−2i2i0000-2-2000022000000000000−2i2i−2i2i00000000000000000000000000−2i2i002-2
χ492-2-2222-2-2222-2-2-2-2-222-222-2-2200002-20000-220000000000002-2-2200000000000000000000002i−2i00002i−2i00
χ502-2-2222-2-2222-2-2-2-2-222-222-2-2200002-20000-220000000000002-2-220000000000000000000000−2i2i0000−2i2i00
χ512-2-2222-2-2222-2-2-2-2-222-22-222-200002-20000-22000000000000-222-200000000000000000000002i−2i0000−2i2i00
χ522-2-2222-2-2222-2-2-2-2-222-22-222-200002-20000-22000000000000-222-20000000000000000000000−2i2i00002i−2i00
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2000044-4-422-2-2-2-222000000000022000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-20000-4-444222222220000000000-2-2000000000000000000000000000000000000
χ55444-4-44-4-44000044-4-44-4-400000000000000000000000000000000000000004-40000000000000000000000
χ56444-4-44-4-44000044-4-44-4-40000000000000000000000000000000000000000-440000000000000000000000
χ5744-44-4-4-44-24-4-44-222-22-2200004i−4i4i−4i-22−2i−2i2i2i-220000000000−2i2i000000000000000000000000000000000000
χ5844-44-4-4-44-24-4-44-222-22-220000−4i4i−4i4i-222i2i−2i−2i-2200000000002i−2i000000000000000000000000000000000000
χ5944-4-44-44-4400004-44-4-4-440000000000000000000000000000000000000000004i−4i00000000000000000000
χ6044-4-44-44-4400004-44-4-4-44000000000000000000000000000000000000000000−4i4i00000000000000000000
χ614-444-4-44-444-44-4-4444-4-4-400000000440000-4-4000000000000000000000000000000000000000000000000
χ624-444-4-44-4-24-44-42-2-2-222200000000-2-200002200−2i32i3−2i32i3000000000000000000000000000000000000000000
χ634-444-4-44-4-24-44-42-2-2-222200000000-2-2000022002i3−2i32i3−2i3000000000000000000000000000000000000000000
χ644-444-4-44-4-2-44-442-2-2-22224i−4i4i−4i0000220000-2-2000000000000−2i2i−2i2i00000000000000000000000000000000
χ654-444-4-44-4-2-44-442-2-2-2222−4i4i−4i4i0000220000-2-20000000000002i−2i2i−2i00000000000000000000000000000000
χ664-44-44-4-4440000-44-4-4-44400000000000000000000000022−22000000000022−2222−22000000000000000000000000
χ674-44-44-4-4440000-44-4-4-444000000000000000000000000−22220000000000−2222−2222000000000000000000000000
χ684-44-44-4-44-200002-2222-2-20000000000−2i32i3−2i32i3000000000022−22000000i6−i6i6−i6−22−22000000000000000000000000
χ694-44-44-4-44-200002-2222-2-20000000000−2i32i3−2i32i30000000000−2222000000−i6i6−i6i62−22−2000000000000000000000000
χ704-44-44-4-44-200002-2222-2-200000000002i3−2i32i3−2i3000000000022−22000000−i6i6−i6i6−22−22000000000000000000000000
χ714-44-44-4-44-200002-2222-2-200000000002i3−2i32i3−2i30000000000−2222000000i6−i6i6−i62−22−2000000000000000000000000
χ724-4-4444-4-44-4-444-4-4-444-4400000000-4400004-4000000000000000000000000000000000000000000000000
χ734-4-4444-4-4-244-4-4222-2-22-24-4-440000-2200002-2000000000000-222-200000000000000000000000000000000
χ744-4-4444-4-4-244-4-4222-2-22-2-444-40000-2200002-20000000000002-2-2200000000000000000000000000000000
χ754-4-4444-4-4-2-4-444222-2-22-2000000002-20000-2200−2i32i32i3−2i3000000000000000000000000000000000000000000
χ764-4-4444-4-4-2-4-444222-2-22-2000000002-20000-22002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ774-4-4-4-444440000-4-44-444-4000000000000000000000022−220000000022−22−22220000000000000000000000000000
χ784-4-4-4-444440000-4-44-444-40000000000000000000000−222200000000−222222−220000000000000000000000000000
χ794-4-4-4-4444-2000022-22-2-22000000000023−23−23230000000022−2200000000−222−2−666−6000000000000000000000000
χ804-4-4-4-4444-2000022-22-2-22000000000023−23−232300000000−2222000000002−2−226−6−66000000000000000000000000
χ814-4-4-4-4444-2000022-22-2-220000000000−232323−230000000022−2200000000−222−26−6−66000000000000000000000000
χ824-4-4-4-4444-2000022-22-2-220000000000−232323−2300000000−2222000000002−2−22−666−6000000000000000000000000
χ83888-8-88-8-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-88-88-8-40000-44-4444-40000000000000000000000000000000000000000000000000000000000000000

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