Finite Group Databasebeta

← Group #10690195

Character table — Group #10690195

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order12222222222236666666444466661212121244444444888812121212121212121212242424242424242422221212121222224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ911-1-111-1-11-1-11111-1-11-1-111-1-11-1-1111-1-1ii−i−i11-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-11-1ii−i−iii−i−i
χ1011-1-111-1-11-1-11111-1-11-1-111-1-11-1-1111-1-1ii−i−i11-1-1ii−i−i1-11111-1-1-1-1iiii−i−i−i−i-1-111ii−i−i-1-111-11−i−iii−i−iii
χ1111-1-111-1-11-1-11111-1-11-1-111-1-11-1-1111-1-1ii−i−i-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-1-1111-1ii−i−i−i−iii
χ1211-1-111-1-11-1-11111-1-11-1-111-1-11-1-1111-1-1ii−i−i-1-111−i−iii1-1-1-1-1-11111−i−i−i−iiiii-1-111ii−i−i11-1-1-11−i−iiiii−i−i
χ1311-1-111-1-11-1-11111-1-11-1-111-1-11-1-1111-1-1−i−iii11-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii11-1-11-1−i−iii−i−iii
χ1411-1-111-1-11-1-11111-1-11-1-111-1-11-1-1111-1-1−i−iii11-1-1−i−iii1-11111-1-1-1-1−i−i−i−iiiii-1-111−i−iii-1-111-11ii−i−iii−i−i
χ1511-1-111-1-11-1-11111-1-11-1-111-1-11-1-1111-1-1−i−iii-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-1-1111-1−i−iiiii−i−i
χ1611-1-111-1-11-1-11111-1-11-1-111-1-11-1-1111-1-1−i−iii-1-111ii−i−i1-1-1-1-1-11111iiii−i−i−i−i-1-111−i−iii11-1-1-11ii−i−i−i−iii
χ1722222222222222222222-2-2-2-22222-2-2-2-2000000000000-2-20000000000000000222200000000-2-200000000
χ1822222222222222222222-2-2-2-22222-2-2-2-2000000000000-2-20000000000000000-2-2-2-2000000002200000000
χ19222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ20222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-111111111111111110000-1-1-1-100000000000000
χ21222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000111100000000000000
χ22222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-10000111100000000000000
χ2322222222-2-2-2-2222222222-22-2-2-2-2-22222000000000000-2-20000000000000000000000000000002-22-20000
χ2422222222-2-2-2-2222222222-22-2-2-2-2-22222000000000000-2-2000000000000000000000000000000-22-220000
χ2522222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-22-22-20000000022000000000000000000002-22-200000000000000
χ2622222222-2-2-2-222222222-22-22-2-2-2-2-2-2-2-2-22-22000000002200000000000000000000-22-2200000000000000
χ2722222222-2-2-2-2-1-1-1-1-1-1-1-1-22-22111111112-22-200000000-1-133−3−333−3−333−3−333−3−30000-11-1100000000000000
χ2822222222-2-2-2-2-1-1-1-1-1-1-1-1-22-22111111112-22-200000000-1-1−3−333−3−333−3−333−3−3330000-11-1100000000000000
χ2922222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211111111-22-2200000000-1-133−3−333−3−3−3−333−3−33300001-11-100000000000000
χ3022222222-2-2-2-2-1-1-1-1-1-1-1-1-22-2211111111-22-2200000000-1-1−3−333−3−33333−3−333−3−300001-11-100000000000000
χ312222-2-2-2-2-22-2222-222-2-2-20000-22-22000000000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i22-22-200000000000000−i2i2−i2i2
χ322222-2-2-2-2-22-2222-222-2-2-20000-22-22000000000000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2-22-2200000000000000i2−i2i2−i2
χ332222-2-2-2-2-22-2222-222-2-2-20000-22-22000000000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i22-22-200000000000000i2−i2i2−i2
χ342222-2-2-2-2-22-2222-222-2-2-20000-22-22000000000000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2-22-2200000000000000−i2i2−i2i2
χ3522-2-222-2-22-2-22222-2-22-2-2-2-2222-2-22-2-222000000000000-22000000000000000022-2-200000000-2200000000
χ3622-2-222-2-22-2-22222-2-22-2-2-2-2222-2-22-2-222000000000000-220000000000000000-2-222000000002-200000000
χ3722-2-222-2-22-2-22-1-1-111-11122-2-2-111-1-1-1112i2i−2i−2i22-2-22i2i−2i−2i-11-1-1-1-11111−i−i−i−iiiii0000−i−iii00000000000000
χ3822-2-222-2-22-2-22-1-1-111-11122-2-2-111-1-1-1112i2i−2i−2i-2-222−2i−2i2i2i-111111-1-1-1-1iiii−i−i−i−i0000−i−iii00000000000000
χ3922-2-222-2-22-2-22-1-1-111-11122-2-2-111-1-1-111−2i−2i2i2i22-2-2−2i−2i2i2i-11-1-1-1-11111iiii−i−i−i−i0000ii−i−i00000000000000
χ4022-2-222-2-22-2-22-1-1-111-11122-2-2-111-1-1-111−2i−2i2i2i-2-2222i2i−2i−2i-111111-1-1-1-1−i−i−i−iiiii0000ii−i−i00000000000000
χ4122-2-222-2-2-222-2222-2-22-2-22-2-22-222-222-2-2000000000000-220000000000000000000000000000002i−2i−2i2i0000
χ4222-2-222-2-2-222-2222-2-22-2-22-2-22-222-222-2-2000000000000-22000000000000000000000000000000−2i2i2i−2i0000
χ4322-2-222-2-2-222-2222-2-22-2-2-222-2-222-2-2-2222i−2i−2i2i000000002-2000000000000000000002i−2i−2i2i00000000000000
χ4422-2-222-2-2-222-2222-2-22-2-2-222-2-222-2-2-222−2i2i2i−2i000000002-200000000000000000000−2i2i2i−2i00000000000000
χ4522-2-222-2-2-222-2-1-1-111-111-222-21-1-1111-1-12i−2i−2i2i00000000-1133−3−3−3−333i3i3−i3−i3−i3−i3i3i30000−iii−i00000000000000
χ4622-2-222-2-2-222-2-1-1-111-111-222-21-1-1111-1-12i−2i−2i2i00000000-11−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000−iii−i00000000000000
χ4722-2-222-2-2-222-2-1-1-111-111-222-21-1-1111-1-1−2i2i2i−2i00000000-1133−3−3−3−333−i3−i3i3i3i3i3−i3−i30000i−i−ii00000000000000
χ4822-2-222-2-2-222-2-1-1-111-111-222-21-1-1111-1-1−2i2i2i−2i00000000-11−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000i−i−ii00000000000000
χ4922-2-2-2-222-2-22222-2-2-2-2220000-2-2220000000000002−2−2200000000002−22−2−22−222-2-22000000000000002−2−22
χ5022-2-2-2-222-2-22222-2-2-2-2220000-2-2220000000000002−2−2200000000002−22−2−22−22-222-200000000000000−222−2
χ5122-2-2-2-222-2-22222-2-2-2-2220000-2-222000000000000−222−20000000000−22−222−22−22-2-2200000000000000−222−2
χ5222-2-2-2-222-2-22222-2-2-2-2220000-2-222000000000000−222−20000000000−22−222−22−2-222-2000000000000002−2−22
χ53444444444444-2-2-2-2-2-2-2-2-4-4-4-4-2-2-2-222220000000000002200000000000000000000000000000000000000
χ5444444444-4-4-4-4-2-2-2-2-2-2-2-24-44-42222-2-2-2-20000000000002200000000000000000000000000000000000000
χ554444-4-4-4-44-44-444-444-4-4-400004-44-400000000000000000000000000000000000000000000000000000000
χ564444-4-4-4-44-44-4-2-22-2-22220000-22-2200000000000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ574444-4-4-4-44-44-4-2-22-2-22220000-22-2200000000000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ584444-4-4-4-4-44-44-2-22-2-222200002-22-2000000000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000
χ594444-4-4-4-4-44-44-2-22-2-222200002-22-20000000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000
χ6044-4-444-4-44-4-44-2-2-222-222-4-444-222-222-2-20000000000002-200000000000000000000000000000000000000
χ6144-4-444-4-4-444-4-2-2-222-2224-4-442-2-22-2-2220000000000002-200000000000000000000000000000000000000
χ6244-4-4-4-44444-4-444-4-4-4-444000044-4-400000000000000000000000000000000000000000000000000000000
χ6344-4-4-4-44444-4-4-2-22222-2-20000-2-222000000000000000000000000006−6−66−666−60000000000000000000000
χ6444-4-4-4-44444-4-4-2-22222-2-20000-2-22200000000000000000000000000−666−66−6−660000000000000000000000
χ6544-4-4-4-444-4-444-2-22222-2-2000022-2-200000000000022−22−22220000000000−22−222−22−20000000000000000000000
χ6644-4-4-4-444-4-444-2-22222-2-2000022-2-2000000000000−222222−2200000000002−22−2−22−220000000000000000000000
χ674-44-44-44-400004-4-44-444-4000000000000000000000000000000000000000000000000002-22-20000000000
χ684-44-44-44-400004-4-44-444-400000000000000000000000000000000000000000000000000-22-220000000000
χ694-44-4-44-4400004-444-4-4-4400000000000000002-22-20000002-22-22-22-2000000000000000000000000000000
χ704-44-4-44-4400004-444-4-4-440000000000000000-22-22000000-22-22-22-22000000000000000000000000000000
χ714-44-4-44-440000-22-2-2222-20000000023−2323−2300002-22-2000000−1+31−3−1−31+3−1+31−3−1−31+3000000000000000000000000000000
χ724-44-4-44-440000-22-2-2222-20000000023−2323−230000-22-220000001−3−1+31+3−1−31−3−1+31+3−1−3000000000000000000000000000000
χ734-44-4-44-440000-22-2-2222-200000000−2323−232300002-22-2000000−1−31+3−1+31−3−1−31+3−1+31−3000000000000000000000000000000
χ744-44-4-44-440000-22-2-2222-200000000−2323−23230000-22-220000001+3−1−31−3−1+31+3−1−31−3−1+3000000000000000000000000000000
χ754-4-444-4-4400004-4-4-444-44000000000000000000000000000000000000000000000000002-2-220000000000
χ764-4-444-4-4400004-4-4-444-4400000000000000000000000000000000000000000000000000-222-20000000000
χ774-4-44-444-400004-44-44-44-400000000000000002-2-220000002-22-2-22-22000000000000000000000000000000
χ784-4-44-444-400004-44-44-44-40000000000000000-222-2000000-22-222-22-2000000000000000000000000000000
χ794-4-44-444-40000-22-22-22-220000000023−23−232300002-2-22000000−1+31−3−1−31+31−3−1+31+3−1−3000000000000000000000000000000
χ804-4-44-444-40000-22-22-22-220000000023−23−23230000-222-20000001−3−1+31+3−1−3−1+31−3−1−31+3000000000000000000000000000000
χ814-4-44-444-40000-22-22-22-2200000000−232323−2300002-2-22000000−1−31+3−1+31−31+3−1−31−3−1+3000000000000000000000000000000
χ824-4-44-444-40000-22-22-22-2200000000−232323−230000-222-20000001+3−1−31−3−1+3−1−31+3−1+31−3000000000000000000000000000000
χ838-88-88-88-80000-444-44-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-888-8-880000-4444-4-44-40000000000000000000000000000000000000000000000000000000000000000

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