Finite Group Databasebeta

← Group #10868041

Character table — Group #10868041

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122222223444444446666666444444121212121212121244888812121212121212121212242424242424242444448888888844121212122444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ811111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-111-1-1
χ91111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-1-1-111-11-1-11111-1-1
χ101111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111-1-1-1111-111-1-1-1-111
χ111111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1111-1-1-11-1-1-1-11111
χ121111111111-1-1-1-11111111111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1111-1-11-11111-1-1-1-1
χ131111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1111-1-1-1111-1-1-1-111
χ141111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1111-1-11-1-1-11111-1-1
χ151111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111-1-1-111-111111-1-1-1-1
χ161111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-11-1-1-1111-1-1-1-1-11111
χ17222222222-22222-2-2-22222222-2-20000-2-22222-2-2000000-2-20000000000000000222200000000000000-2-200000000
χ18222222222-22222-2-2-22222222-2-20000-2-22222-2-2000000-2-20000000000000000-2-2-2-2000000000000002200000000
χ19222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-200000022000000000000000022-2-2000000000000002-200000000
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-2-2-2-2-2-2-2000000220000000000000000-2-22200000000000000-2200000000
χ2122222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111100000000000022-1-1-1-10000000000
χ2522222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-222-2-211-1-1-1-11111-1-1-1-111110000000000002-211-1-10000000000
χ2622222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-22222-1-11111-1-1-2-2-2-22211-1-1-1-111111111-1-1-1-1000000000000-22-1-1110000000000
χ2722222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12222-2-2111111-1-1-1-1-1-1-1-11111000000000000-22-1-1110000000000
χ2822222222-12-2-2-2-2222-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-122-2-222111111-1-1-1-11111-1-1-1-10000000000002-211-1-10000000000
χ2922-2-22-2-22222i2i−2i−2i-2-222-2-222-2-22i−2i00002-22i2i−2i−2i2-20000002i−2i0000000000000000000000000000000000002i−2i002-200
χ3022-2-22-2-22222i2i−2i−2i-2-222-2-222-2-22i−2i00002-22i2i−2i−2i2-20000002i−2i000000000000000000000000000000000000−2i2i00-2200
χ3122-2-22-2-2222−2i−2i2i2i-2-222-2-222-2-2−2i2i00002-2−2i−2i2i2i2-2000000−2i2i0000000000000000000000000000000000002i−2i00-2200
χ3222-2-22-2-2222−2i−2i2i2i-2-222-2-222-2-2−2i2i00002-2−2i−2i2i2i2-2000000−2i2i000000000000000000000000000000000000−2i2i002-200
χ3322-2-22-2-222-22i2i−2i−2i22-22-2-222-2-2−2i2i2i2i−2i−2i-222i2i−2i−2i-222-20000−2i2i2i2i−2i−2i22-2-2000000000000000000000000000000000000
χ3422-2-22-2-222-22i2i−2i−2i22-22-2-222-2-2−2i2i−2i−2i2i2i-222i2i−2i−2i-22-220000−2i2i−2i−2i2i2i-2-222000000000000000000000000000000000000
χ3522-2-22-2-222-2−2i−2i2i2i22-22-2-222-2-22i−2i2i2i−2i−2i-22−2i−2i2i2i-22-2200002i−2i2i2i−2i−2i-2-222000000000000000000000000000000000000
χ3622-2-22-2-222-2−2i−2i2i2i22-22-2-222-2-22i−2i−2i−2i2i2i-22−2i−2i2i2i-222-200002i−2i−2i−2i2i2i22-2-2000000000000000000000000000000000000
χ3722-2-22-2-22-1-22i2i−2i−2i22-2-111-1-111−2i2i2i2i−2i−2i1-1−i−iii1-12-20000i−i−i−iii-1-111−i3−i3i3i333−3−300000000000000−i3i33−30000000000
χ3822-2-22-2-22-1-22i2i−2i−2i22-2-111-1-111−2i2i2i2i−2i−2i1-1−i−iii1-12-20000i−i−i−iii-1-111i3i3−i3−i3−3−33300000000000000i3−i3−330000000000
χ3922-2-22-2-22-1-22i2i−2i−2i22-2-111-1-111−2i2i−2i−2i2i2i1-1−i−iii1-1-220000i−iii−i−i11-1-1−i3−i3i3i333−3−300000000000000i3−i3−330000000000
χ4022-2-22-2-22-1-22i2i−2i−2i22-2-111-1-111−2i2i−2i−2i2i2i1-1−i−iii1-1-220000i−iii−i−i11-1-1i3i3−i3−i3−3−33300000000000000−i3i33−30000000000
χ4122-2-22-2-22-1-2−2i−2i2i2i22-2-111-1-1112i−2i2i2i−2i−2i1-1ii−i−i1-1-220000−ii−i−iii11-1-1−i3−i3i3i3−3−33300000000000000i3−i33−30000000000
χ4222-2-22-2-22-1-2−2i−2i2i2i22-2-111-1-1112i−2i2i2i−2i−2i1-1ii−i−i1-1-220000−ii−i−iii11-1-1i3i3−i3−i333−3−300000000000000−i3i3−330000000000
χ4322-2-22-2-22-1-2−2i−2i2i2i22-2-111-1-1112i−2i−2i−2i2i2i1-1ii−i−i1-12-20000−iiii−i−i-1-111−i3−i3i3i3−3−33300000000000000−i3i3−330000000000
χ4422-2-22-2-22-1-2−2i−2i2i2i22-2-111-1-1112i−2i−2i−2i2i2i1-1ii−i−i1-12-20000−iiii−i−i-1-111i3i3−i3−i333−3−300000000000000i3−i33−30000000000
χ452-222-2-2-22202i−2i2i−2i000-22-22-22-2000000002i−2i2i−2i0000−i2i22−20000000000−i2i2−i2i22−22−22-22i−2i−i2−i2i2i222−2−20000000000000000
χ462-222-2-2-22202i−2i2i−2i000-22-22-22-2000000002i−2i2i−2i0000−i2i22−20000000000−i2i2−i2i22−22−2-22−2i2ii2i2−i2−i2−2−2220000000000000000
χ472-222-2-2-22202i−2i2i−2i000-22-22-22-2000000002i−2i2i−2i0000i2−i2−220000000000i2−i2i2−i2−22−222-22i−2ii2i2−i2−i2−2−2220000000000000000
χ482-222-2-2-22202i−2i2i−2i000-22-22-22-2000000002i−2i2i−2i0000i2−i2−220000000000i2−i2i2−i2−22−22-22−2i2i−i2−i2i2i222−2−20000000000000000
χ492-222-2-2-2220−2i2i−2i2i000-22-22-22-200000000−2i2i−2i2i0000−i2i2−220000000000−i2i2−i2i2−22−222-2−2i2i−i2−i2i2i2−2−2220000000000000000
χ502-222-2-2-2220−2i2i−2i2i000-22-22-22-200000000−2i2i−2i2i0000−i2i2−220000000000−i2i2−i2i2−22−22-222i−2ii2i2−i2−i222−2−20000000000000000
χ512-222-2-2-2220−2i2i−2i2i000-22-22-22-200000000−2i2i−2i2i0000i2−i22−20000000000i2−i2i2−i22−22−22-2−2i2ii2i2−i2−i222−2−20000000000000000
χ522-222-2-2-2220−2i2i−2i2i000-22-22-22-200000000−2i2i−2i2i0000i2−i22−20000000000i2−i2i2−i22−22−2-222i−2i−i2−i2i2i2−2−2220000000000000000
χ532-22-222-2-22200002-2-2-2-2-2-2222002-22-22-20000-22000000002-22-200000000000000002i−2i2i−2i000000000000002i−2i0000
χ542-22-222-2-22200002-2-2-2-2-2-2222002-22-22-20000-22000000002-22-20000000000000000−2i2i−2i2i00000000000000−2i2i0000
χ552-22-222-2-22200002-2-2-2-2-2-222200-22-222-20000-2200000000-22-2200000000000000002i−2i2i−2i00000000000000−2i2i0000
χ562-22-222-2-22200002-2-2-2-2-2-222200-22-222-20000-2200000000-22-220000000000000000−2i2i−2i2i000000000000002i−2i0000
χ572-2-222-22-22-200002-22-222-22-2-2002i−2i−2i2i-2-2000022000000002i−2i−2i2i000000000000000000002-22-2000000000000002i−2i
χ582-2-222-22-22-200002-22-222-22-2-2002i−2i−2i2i-2-2000022000000002i−2i−2i2i00000000000000000000-22-2200000000000000−2i2i
χ592-2-222-22-22-200002-22-222-22-2-200−2i2i2i−2i-2-200002200000000−2i2i2i−2i000000000000000000002-22-200000000000000−2i2i
χ602-2-222-22-22-200002-22-222-22-2-200−2i2i2i−2i-2-200002200000000−2i2i2i−2i00000000000000000000-22-22000000000000002i−2i
χ6144444444-2-44444-4-4-4-2-2-2-2-2-2-2-4-4000022-2-2-2-2220000002200000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-244000022222222000000-2-200000000000000000000000000000000000000000000
χ63444-4-4-44-44000000004-44-4-44-400000000000000000000000000000000000000000022−22−222200000000000000000000
χ64444-4-4-44-44000000004-44-4-44-4000000000000000000000000000000000000000000−222222−2200000000000000000000
χ6544-44-44-4-440000000044-4-4-4-44000000000000000000000000000000000000000000000022−22−22220000000000000000
χ6644-44-44-4-440000000044-4-4-4-440000000000000000000000000000000000000000000000−222222−220000000000000000
χ6744-4-44-4-44-244i4i−4i−4i-4-44-222-2-2224i−4i0000-22−2i−2i2i2i-22000000−2i2i00000000000000000000000000000000000000000000
χ6844-4-44-4-44-24−4i−4i4i4i-4-44-222-2-222−4i4i0000-222i2i−2i−2i-220000002i−2i00000000000000000000000000000000000000000000
χ694-444-4-4-44-204i−4i4i−4i0002-22-22-2200000000−2i2i−2i2i0000−2i22i222−220000000000i2−i2i2−i2−22−220000000000000000000000000000
χ704-444-4-4-44-204i−4i4i−4i0002-22-22-2200000000−2i2i−2i2i00002i2−2i2−22220000000000−i2i2−i2i22−22−20000000000000000000000000000
χ714-444-4-4-44-20−4i4i−4i4i0002-22-22-22000000002i−2i2i−2i0000−2i22i2−22220000000000i2−i2i2−i22−22−20000000000000000000000000000
χ724-444-4-4-44-20−4i4i−4i4i0002-22-22-22000000002i−2i2i−2i00002i2−2i222−220000000000−i2i2−i2i2−22−220000000000000000000000000000
χ734-44-444-4-44-40000-444-4-4-4-4444000000-4400004-40000000000000000000000000000000000000000000000000000
χ744-44-444-4-4-2400004-4-42222-2-2-2004-44-4-2200002-200000000-22-220000000000000000000000000000000000000000
χ754-44-444-4-4-2400004-4-42222-2-2-200-44-44-2200002-2000000002-22-20000000000000000000000000000000000000000
χ764-44-444-4-4-2-40000-4442222-2-2-20000002-20000-22000000000000−2i32i3−2i32i3000000000000000000000000000000000000
χ774-44-444-4-4-2-40000-4442222-2-2-20000002-20000-220000000000002i3−2i32i3−2i3000000000000000000000000000000000000
χ784-4-444-44-4440000-44-4-444-44-4-4000000440000-4-40000000000000000000000000000000000000000000000000000
χ794-4-444-44-4-240000-44-42-2-22-222000000-2-2000022000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ804-4-444-44-4-240000-44-42-2-22-222000000-2-20000220000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ814-4-444-44-4-2-400004-442-2-22-222004i−4i−4i4i220000-2-200000000−2i2i2i−2i0000000000000000000000000000000000000000
χ824-4-444-44-4-2-400004-442-2-22-22200−4i4i4i−4i220000-2-2000000002i−2i−2i2i0000000000000000000000000000000000000000
χ834-4-4-4-4444404-4-44000-4-444-4-44000000004-4-44000000000000000000000000000000000000000000000000000000
χ844-4-4-4-444440-444-4000-4-444-4-4400000000-444-4000000000000000000000000000000000000000000000000000000
χ854-4-4-4-4444-204-4-4400022-2-222-200000000-222-20000000000000000006−6−666−6−660000000000000000000000000000
χ864-4-4-4-4444-204-4-4400022-2-222-200000000-222-2000000000000000000−666−6−666−60000000000000000000000000000
χ874-4-4-4-4444-20-444-400022-2-222-2000000002-2-220000000000000000006−6−66−666−60000000000000000000000000000
χ884-4-4-4-4444-20-444-400022-2-222-2000000002-2-22000000000000000000−666−66−6−660000000000000000000000000000
χ89888-8-8-88-8-400000000-44-444-44000000000000000000000000000000000000000000000000000000000000000000
χ9088-88-88-8-8-400000000-4-44444-4000000000000000000000000000000000000000000000000000000000000000000

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