Finite Group Databasebeta

← Group #10690187

Character table — Group #10690187

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222222222444444448888888888888888888888888888888888888824242424242424242424242424242424
order1222222222223666666666666666444444444444444444121212121212121212121212121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911-1-111-1-11-1-111111-1-1-1-1-1-1-1-1111111-1-111-1-11-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-111-1-11-1-111111-1-1-1-1-1-1-1-1111111-1-111-1-11-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-111-1-11-1-111111-1-1-1-1-1-1-1-1111111-1-111-1-11-1-1-111-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-111-1-11-1-111111-1-1-1-1-1-1-1-1111111-1-111-1-11-1-1-111-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-111-1-11-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411-1-111-1-11-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511-1-111-1-11-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ1611-1-111-1-11-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222222222222222-2-2-2-2-2-200000000222200000000-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222222222222222222222222-2-2-2-2-2-2-2-22200000000-2-2-2-200000000-2-2-2-22222000000000000000000000000
χ19222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111111110000000000000000
χ21222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-200000000-1-1-1-1−i3−i3i3i3−i3−i3i3i311111111−i3−i3i3i3−i3−i3i3i30000000000000000
χ22222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-200000000-1-1-1-1i3i3−i3−i3i3i3−i3−i311111111i3i3−i3−i3i3i3−i3−i30000000000000000
χ23222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-22222-2-2-2-2111111111111-1-1-1-11111-1-1-1-1-1-1-1-10000000000000000
χ24222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-222221111-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000
χ25222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222000000001111−i3−i3i3i3−i3−i3i3i31111-1-1-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ26222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222000000001111i3i3−i3−i3i3i3−i3−i31111-1-1-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222222-2-2-2-222-2-22222-2-2-2-22-2-2200002-22-200000000000000000000002-22-200000000000000002-22-200000000
χ2822222222-2-2-2-222-2-22222-2-2-2-22-2-2200002-22-200000000000000000000002-22-20000000000000000-22-2200000000
χ2922222222-2-2-2-222-2-22222-2-2-2-22-2-220000-22-220000000000000000000000-22-220000000000002-22-2000000000000
χ3022222222-2-2-2-222-2-22222-2-2-2-22-2-220000-22-220000000000000000000000-22-22000000000000-22-22000000000000
χ3122-2-222-2-22-2-222222-2-2-2-2-2-2-2-2222222-2-2-2-222-220000000022-2-200000000-2-222-2-222000000000000000000000000
χ3222-2-222-2-22-2-222222-2-2-2-2-2-2-2-22222-2-222-2-2222-200000000-2-22200000000-2-22222-2-2000000000000000000000000
χ3322-2-222-2-22-2-22-1-1-1-111111111-1-1-1-122-2-222-2-22-222-2-222-2-2-1-111-1-1-1-11111-1-111-1-111-1-1-1-111110000000000000000
χ3422-2-222-2-22-2-22-1-1-1-111111111-1-1-1-122-2-222-2-22-2-2-222-2-222-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-10000000000000000
χ3522-2-222-2-22-2-22-1-1-1-111111111-1-1-1-122-2-2-2-222-2200000000-1-111−i3−i3i3i3i3i3−i3−i311-1-111-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ3622-2-222-2-22-2-22-1-1-1-111111111-1-1-1-122-2-2-2-222-2200000000-1-111i3i3−i3−i3−i3−i3i3i311-1-111-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ3722-2-222-2-22-2-22-1-1-1-111111111-1-1-1-1-2-22222-2-2-2222-2-2-2-22211-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111110000000000000000
χ3822-2-222-2-22-2-22-1-1-1-111111111-1-1-1-1-2-22222-2-2-22-2-22222-2-211-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-10000000000000000
χ3922-2-222-2-22-2-22-1-1-1-111111111-1-1-1-1-2-222-2-2222-20000000011-1-1−i3−i3i3i3i3i3−i3−i311-1-1-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ4022-2-222-2-22-2-22-1-1-1-111111111-1-1-1-1-2-222-2-2222-20000000011-1-1i3i3−i3−i3−i3−i3i3i311-1-1-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ4122-2-222-2-2-222-222-2-2-2-2-2-222222-2-2200002-2-2200000000000000000000002-2-2200000000000000002i−2i−2i2i00000000
χ4222-2-222-2-2-222-222-2-2-2-2-2-222222-2-2200002-2-2200000000000000000000002-2-220000000000000000−2i2i2i−2i00000000
χ4322-2-222-2-2-222-222-2-2-2-2-2-222222-2-220000-222-20000000000000000000000-222-20000000000002i−2i−2i2i000000000000
χ4422-2-222-2-2-222-222-2-2-2-2-2-222222-2-220000-222-20000000000000000000000-222-2000000000000−2i2i2i−2i000000000000
χ452-2222-2-2-222-2-22-22222-2-222-2-22-2-2-22-22-2000000000000002-22-2000000000000000000000000000000002−22−22−22−2
χ462-2222-2-2-222-2-22-22222-2-222-2-22-2-2-22-22-2000000000000002-22-200000000000000000000000000000000−22−22−22−22
χ472-2222-2-2-222-2-22-22222-2-222-2-22-2-2-2-22-2200000000000000-22-22000000000000000000000000000000002−22−2−22−22
χ482-2222-2-2-222-2-22-22222-2-222-2-22-2-2-2-22-2200000000000000-22-2200000000000000000000000000000000−22−222−22−2
χ492-2-2-22-2222-22-22-222-2-222-2-2222-2-2-22-2-22000000000000002-2-2200000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ502-2-2-22-2222-22-22-222-2-222-2-2222-2-2-22-2-22000000000000002-2-2200000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ512-2-2-22-2222-22-22-222-2-222-2-2222-2-2-2-222-200000000000000-222-200000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ522-2-2-22-2222-22-22-222-2-222-2-2222-2-2-2-222-200000000000000-222-200000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ5344444444-4-4-4-4-2-222-2-2-2-22222-222-200004-44-40000000000000000000000-22-220000000000000000000000000000
χ5444444444-4-4-4-4-2-222-2-2-2-22222-222-20000-44-4400000000000000000000002-22-20000000000000000000000000000
χ55444-4-4-44-4000044004-44-40000-400-4000000000000002-22-200002-22-22-22-200000000000000000000000000000000
χ56444-4-4-44-4000044004-44-40000-400-400000000000000-22-220000-22-22-22-2200000000000000000000000000000000
χ57444-4-4-44-40000-2-2−2i32i3-22-22−2i32i3−2i32i32−2i32i32000000000000002-22-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000000000000000
χ58444-4-4-44-40000-2-2−2i32i3-22-22−2i32i3−2i32i32−2i32i3200000000000000-22-2200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000000000000000
χ59444-4-4-44-40000-2-22i3−2i3-22-222i3−2i32i3−2i322i3−2i32000000000000002-22-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000000000000000
χ60444-4-4-44-40000-2-22i3−2i3-22-222i3−2i32i3−2i322i3−2i3200000000000000-22-2200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000000000000000
χ6144-44-4-4-4400004400-44-440000-400-4000000000000002-2-2200002-22-2-22-2200000000000000000000000000000000
χ6244-44-4-4-4400004400-44-440000-400-400000000000000-222-20000-22-222-22-200000000000000000000000000000000
χ6344-44-4-4-440000-2-2−2i32i32-22-22i3−2i32i3−2i32−2i32i32000000000000002-2-220000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000000000000000
χ6444-44-4-4-440000-2-2−2i32i32-22-22i3−2i32i3−2i32−2i32i3200000000000000-222-200001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000000000000000
χ6544-44-4-4-440000-2-22i3−2i32-22-2−2i32i3−2i32i322i3−2i32000000000000002-2-220000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000000000
χ6644-44-4-4-440000-2-22i3−2i32-22-2−2i32i3−2i32i322i3−2i3200000000000000-222-200001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000000000000000
χ6744-4-444-4-4-444-4-2-2222222-2-2-2-2-222-200004-4-440000000000000000000000-222-20000000000000000000000000000
χ6844-4-444-4-4-444-4-2-2222222-2-2-2-2-222-20000-444-400000000000000000000002-2-220000000000000000000000000000
χ694-4444-4-4-444-4-4-22-2-2-2-222-2-222-22224-44-400000000000000-22-220000000000000000000000000000000000000000
χ704-4444-4-4-444-4-4-22-2-2-2-222-2-222-2222-44-44000000000000002-22-20000000000000000000000000000000000000000
χ714-4444-4-4-4-4-4444-4-4-444-4-4-4-444444-400000000000000000000000000000000000000000000000000000000000000
χ724-4444-4-4-4-4-444-2222-2-22222-2-2-2-2-22000000000000000000000000000000000023−2323−23000000000000000000000000
χ734-4444-4-4-4-4-444-2222-2-22222-2-2-2-2-220000000000000000000000000000000000−2323−2323000000000000000000000000
χ744-44-4-44-4400004-4004-4-440000-400400000000002-22-20000000000000000000000002-22-22-22-20000000000000000
χ754-44-4-44-4400004-4004-4-440000-40040000000000-22-22000000000000000000000000-22-22-22-220000000000000000
χ764-44-4-44-440000-22−2i32i3-222-2−2i32i32i3−2i322i3−2i3-200000000002-22-2000000000000000000000000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000
χ774-44-4-44-440000-22−2i32i3-222-2−2i32i32i3−2i322i3−2i3-20000000000-22-220000000000000000000000001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000
χ784-44-4-44-440000-222i3−2i3-222-22i3−2i3−2i32i32−2i32i3-200000000002-22-2000000000000000000000000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000
χ794-44-4-44-440000-222i3−2i3-222-22i3−2i3−2i32i32−2i32i3-20000000000-22-220000000000000000000000001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000
χ804-4-44-444-400004-400-444-40000-400400000000002-2-220000000000000000000000002-22-2-22-220000000000000000
χ814-4-44-444-400004-400-444-40000-40040000000000-222-2000000000000000000000000-22-222-22-20000000000000000
χ824-4-44-444-40000-22−2i32i32-2-222i3−2i3−2i32i322i3−2i3-200000000002-2-22000000000000000000000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000
χ834-4-44-444-40000-22−2i32i32-2-222i3−2i3−2i32i322i3−2i3-20000000000-222-20000000000000000000000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000
χ844-4-44-444-40000-222i3−2i32-2-22−2i32i32i3−2i32−2i32i3-200000000002-2-22000000000000000000000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000
χ854-4-44-444-40000-222i3−2i32-2-22−2i32i32i3−2i32−2i32i3-20000000000-222-20000000000000000000000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000
χ864-4-4-44-4444-44-4-22-2-222-2-222-2-2-22224-4-4400000000000000-222-20000000000000000000000000000000000000000
χ874-4-4-44-4444-44-4-22-2-222-2-222-2-2-2222-444-4000000000000002-2-220000000000000000000000000000000000000000
χ884-4-4-44-444-44-444-4-4-4-4-44444-4-4444-400000000000000000000000000000000000000000000000000000000000000
χ894-4-4-44-444-44-44-222222-2-2-2-222-2-2-22000000000000000000000000000000000023−23−2323000000000000000000000000
χ904-4-4-44-444-44-44-222222-2-2-2-222-2-2-220000000000000000000000000000000000−232323−23000000000000000000000000

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