Finite Group Databasebeta

← Group #10690321

Character table — Group #10690321

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order122222222222366666664444666612121212222244446666666688881212242424242424242444441212121222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ911-11-11-1-111-1-1111-1-11-1-11-1-1111-1-111-1-111-1-1i−ii−i1111-1-1-1-1ii−i−i1-1iiii−i−i−i−iii−i−iii−i−i1-1i−i1-1ii−i−i11-1-1
χ1011-11-11-1-111-1-1111-1-11-1-11-1-1111-1-111-1-111-1-1i−ii−i1111-1-1-1-1ii−i−i1-1iiii−i−i−i−i−i−iiiii−i−i-11−ii-11−i−iii-1-111
χ1111-11-11-1-111-1-1111-1-11-1-11-1-1111-1-111-1-111-1-1−ii−ii1111-1-1-1-1−i−iii1-1−i−i−i−iiiiiii−i−i−i−iii-11i−i-11ii−i−i-1-111
χ1211-11-11-1-111-1-1111-1-11-1-11-1-1111-1-111-1-111-1-1−ii−ii1111-1-1-1-1−i−iii1-1−i−i−i−iiiii−i−iii−i−iii1-1−ii1-1−i−iii11-1-1
χ1311-11-11-1-111-1-1111-1-11-1-11-1-1111-1-111-1-1-1-111i−ii−i-1-1-1-11111−i−iii1-1−i−i−i−iiiiiii−i−iii−i−i1-1i−i1-1−i−iii-1-111
χ1411-11-11-1-111-1-1111-1-11-1-11-1-1111-1-111-1-1-1-111i−ii−i-1-1-1-11111−i−iii1-1−i−i−i−iiiii−i−iiiii−i−i-11−ii-11ii−i−i11-1-1
χ1511-11-11-1-111-1-1111-1-11-1-11-1-1111-1-111-1-1-1-111−ii−ii-1-1-1-11111ii−i−i1-1iiii−i−i−i−iii−i−i−i−iii-11i−i-11−i−iii11-1-1
χ1611-11-11-1-111-1-1111-1-11-1-11-1-1111-1-111-1-1-1-111−ii−ii-1-1-1-11111ii−i−i1-1iiii−i−i−i−i−i−iii−i−iii1-1−ii1-1ii−i−i-1-111
χ1722222222222222222222-2-2-2-22222-2-2-2-200000000000000000000-2-2000000002222000000-2-20000000000
χ1822222222222222222222-2-2-2-22222-2-2-2-200000000000000000000-2-200000000-2-2-2-2000000220000000000
χ19222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ20222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000111100000000000000
χ21222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2222211111111-2-2-2-2-1-1111111110000-1-1-1-100000000000000
χ22222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111112222-1-1-1-1-1-1-1-1-1-10000111100000000000000
χ2322222222-2-2-2-2222222222-22-2-2-2-2-22222000022-2-2000000000000-2-20000000000002-22-200000000000000
χ2422222222-2-2-2-2222222222-22-2-2-2-2-222220000-2-222000000000000-2-2000000000000-22-2200000000000000
χ2522222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-2000000000000000000002200000000000000002200-2-200000000
χ2622222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-200000000000000000000220000000000000000-2-2002200000000
χ2722222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-1000022-2-2−i3−i3i3i3−i3−i3i3i3000011−i3−i3i3i3−i3−i3i3i30000-11-1100000000000000
χ2822222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-1000022-2-2i3i3−i3−i3i3i3−i3−i3000011i3i3−i3−i3i3i3−i3−i30000-11-1100000000000000
χ2922222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-10000-2-222−i3−i3i3i3−i3−i3i3i3000011i3i3−i3−i3i3i3−i3−i300001-11-100000000000000
χ3022222222-2-2-2-2-1-1-1-1-1-1-1-12-22-21111-1-1-1-10000-2-222i3i3−i3−i3i3i3−i3−i3000011−i3−i3i3i3−i3−i3i3i300001-11-100000000000000
χ3122-22-22-2-222-2-2222-2-22-2-2-222-222-2-2-2-22200000000000000000000-22000000002i2i−2i−2i000000−2i2i0000000000
χ3222-22-22-2-222-2-2222-2-22-2-2-222-222-2-2-2-22200000000000000000000-2200000000−2i−2i2i2i0000002i−2i0000000000
χ3322-22-22-2-222-2-2-1-1-111-1112-2-22-1-111-1-11122-2-22i−2i2i−2i-1-1-1-111112i2i−2i−2i-11−i−i−i−iiiii0000−i−iii00000000000000
χ3422-22-22-2-222-2-2-1-1-111-1112-2-22-1-111-1-11122-2-2−2i2i−2i2i-1-1-1-11111−2i−2i2i2i-11iiii−i−i−i−i0000ii−i−i00000000000000
χ3522-22-22-2-222-2-2-1-1-111-1112-2-22-1-111-1-111-2-2222i−2i2i−2i1111-1-1-1-1−2i−2i2i2i-11iiii−i−i−i−i0000−i−iii00000000000000
χ3622-22-22-2-222-2-2-1-1-111-1112-2-22-1-111-1-111-2-222−2i2i−2i2i1111-1-1-1-12i2i−2i−2i-11−i−i−i−iiiii0000ii−i−i00000000000000
χ3722-22-22-2-2-2-222222-2-22-2-222-2-2-2-22222-2-200002i−2i−2i2i000000000000-220000000000002i−2i−2i2i00000000000000
χ3822-22-22-2-2-2-222222-2-22-2-222-2-2-2-22222-2-20000−2i2i2i−2i000000000000-22000000000000−2i2i2i−2i00000000000000
χ3922-22-22-2-2-2-222222-2-22-2-2-2-222-2-222-2-222000000000000000000002-200000000000000002-200-2200000000
χ4022-22-22-2-2-2-222222-2-22-2-2-2-222-2-222-2-222000000000000000000002-20000000000000000-22002-200000000
χ4122-22-22-2-2-2-222-1-1-111-11122-2-211-1-1-1-11100002i−2i−2i2i−i3−i3i3i3i3i3−i3−i300001-133−3−3−3−3330000−iii−i00000000000000
χ4222-22-22-2-2-2-222-1-1-111-11122-2-211-1-1-1-11100002i−2i−2i2ii3i3−i3−i3−i3−i3i3i300001-1−3−33333−3−30000−iii−i00000000000000
χ4322-22-22-2-2-2-222-1-1-111-11122-2-211-1-1-1-1110000−2i2i2i−2i−i3−i3i3i3i3i3−i3−i300001-1−3−33333−3−30000i−i−ii00000000000000
χ4422-22-22-2-2-2-222-1-1-111-11122-2-211-1-1-1-1110000−2i2i2i−2ii3i3−i3−i3−i3−i3i3i300001-133−3−3−3−3330000i−i−ii00000000000000
χ452-22-2-222-22-22-222-222-2-2-200002-22-200000000000000000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i22i−2i2i−2i000000000000002−22−2
χ462-22-2-222-22-22-222-222-2-2-200002-22-200000000000000000000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i00000000000000−22−22
χ472-22-2-222-22-22-222-222-2-2-200002-22-200000000000000000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00000000000000−22−22
χ482-22-2-222-22-22-222-222-2-2-200002-22-200000000000000000000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i000000000000002−22−2
χ492-2-2-222-222-2-2222-2-2-2-22200002-2-22000000000000000000002−2−22002−22−2−22−222-2-2200000000000000−222−2
χ502-2-2-222-222-2-2222-2-2-2-22200002-2-22000000000000000000002−2−22002−22−2−22−22-222-2000000000000002−2−22
χ512-2-2-222-222-2-2222-2-2-2-22200002-2-2200000000000000000000−222−200−22−222−22−22-2-22000000000000002−2−22
χ522-2-2-222-222-2-2222-2-2-2-22200002-2-2200000000000000000000−222−200−22−222−22−2-222-200000000000000−222−2
χ53444444444444-2-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000000000000000022000000000000000000000000000000
χ5444444444-4-4-4-4-2-2-2-2-2-2-2-2-44-442222222200000000000000000000-2-2000000000000000000000000000000
χ55444-44-4-4-400004-444-4-44-4000000000000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ56444-44-4-4-400004-444-4-44-400000000000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ5744-44-44-4-444-4-4-2-2-222-222-444-4-2-22222-2-2000000000000000000002-2000000000000000000000000000000
χ5844-44-44-4-4-4-444-2-2-222-222-4-44422-2-222-2-200000000000000000000-22000000000000000000000000000000
χ5944-4-4-4-44400004-44-44-4-44000000000000000000000000000000000000000000000000000000002-2-220000
χ6044-4-4-4-44400004-44-44-4-4400000000000000000000000000000000000000000000000000000000-222-20000
χ614-444-4-4-4400004-4-44-44-440000000000002-22-200002-22-22-22-2000000000000000000000000000000000000
χ624-444-4-4-4400004-4-44-44-44000000000000-22-220000-22-22-22-22000000000000000000000000000000000000
χ634-444-4-4-440000-222-22-22-200000000−2i32i3−2i32i32-22-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000000000000000
χ644-444-4-4-440000-222-22-22-200000000−2i32i3−2i32i3-22-2200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000000000000000
χ654-444-4-4-440000-222-22-22-2000000002i3−2i32i3−2i32-22-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000000000000000
χ664-444-4-4-440000-222-22-22-2000000002i3−2i32i3−2i3-22-2200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000000000000000
χ674-44-4-444-44-44-4-2-22-2-22220000-22-2200000000000000000000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i20000000000000000000000
χ684-44-4-444-44-44-4-2-22-2-22220000-22-22000000000000000000002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i20000000000000000000000
χ694-44-4-444-4-44-4444-444-4-4-40000-44-4400000000000000000000000000000000000000000000000000000000
χ704-44-4-444-4-44-44-2-22-2-222200002-22-2000000000000000000000000006−6−666−6−660000000000000000000000
χ714-44-4-444-4-44-44-2-22-2-222200002-22-200000000000000000000000000−666−6−666−60000000000000000000000
χ724-4-444-44-400004-4-4-4444-40000000000002-2-2200002-22-2-22-22000000000000000000000000000000000000
χ734-4-444-44-400004-4-4-4444-4000000000000-222-20000-22-222-22-2000000000000000000000000000000000000
χ744-4-444-44-40000-2222-2-2-2200000000−2i32i32i3−2i32-2-220000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3000000000000000000000000000000000000
χ754-4-444-44-40000-2222-2-2-2200000000−2i32i32i3−2i3-222-200001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000000000000000000
χ764-4-444-44-40000-2222-2-2-22000000002i3−2i3−2i32i32-2-220000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3000000000000000000000000000000000000
χ774-4-444-44-40000-2222-2-2-22000000002i3−2i3−2i32i3-222-200001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000000000000000000
χ784-4-4-444-444-4-44-2-22222-2-20000-222-20000000000000000000022−22−222200−22−222−22−20000000000000000000000
χ794-4-4-444-444-4-44-2-22222-2-20000-222-200000000000000000000−222222−22002−22−2−22−220000000000000000000000
χ804-4-4-444-44-444-444-4-4-4-4440000-444-400000000000000000000000000000000000000000000000000000000
χ814-4-4-444-44-444-4-2-22222-2-200002-2-2200000000000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000
χ824-4-4-444-44-444-4-2-22222-2-200002-2-2200000000000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000
χ83888-88-8-8-80000-44-4-444-440000000000000000000000000000000000000000000000000000000000000000
χ8488-8-8-8-8880000-44-44-444-40000000000000000000000000000000000000000000000000000000000000000

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