Finite Group Databasebeta

← Group #10690177

Character table — Group #10690177

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222222222444444448888888888888888888888888888888888888824242424242424242424242424242424
order122222222222366666666666666622224444444444444466661212121212121212121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911-1-111-1-11-1-111111-1-1-1-1-1-1-1-1111111-1-111-1-11-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-111-1-11-1-111111-1-1-1-1-1-1-1-1111111-1-111-1-11-111-1-111-1-111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-111-1-11-1-111111-1-1-1-1-1-1-1-1111111-1-111-1-11-1-1-111-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-111-1-11-1-111111-1-1-1-1-1-1-1-1111111-1-111-1-11-1-1-111-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-111-1-11-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111111-1-11111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411-1-111-1-11-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111111-1-11111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511-1-111-1-11-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ1611-1-111-1-11-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-11-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222222222222222-2-2-2-2-2-2000000002222-2-2-2-200000000-2-2-2-2000000000000000000000000
χ182222222222222222222222222222-2-2-2-2-2-2-2-22200000000-2-2-2-2222200000000-2-2-2-2000000000000000000000000
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
χ20222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1111111110000000000000000
χ21222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-200000000-1-1-1-11111−i3−i3i3i3−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i30000000000000000
χ22222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-200000000-1-1-1-11111i3i3−i3−i3i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i30000000000000000
χ23222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-22222-2-2-2-21111111111111111-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ24222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000
χ25222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222000000001111-1-1-1-1−i3−i3i3i3−i3−i3i3i31111i3i3−i3−i3i3i3−i3−i30000000000000000
χ26222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222000000001111-1-1-1-1i3i3−i3−i3i3i3−i3−i31111−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222222-2-2-2-222-2-22222-2-2-2-22-2-2200002-22-2000000000000000000000000002-22-20000000000002-22-200000000
χ2822222222-2-2-2-222-2-22222-2-2-2-22-2-2200002-22-2000000000000000000000000002-22-2000000000000-22-2200000000
χ2922222222-2-2-2-222-2-22222-2-2-2-22-2-220000-22-2200000000000000000000000000-22-22000000002-22-2000000000000
χ3022222222-2-2-2-222-2-22222-2-2-2-22-2-220000-22-2200000000000000000000000000-22-2200000000-22-22000000000000
χ312222-2-2-2-222-2-2222222-2-222-2-2-2-2-2-22-22-2000000000000002-22-2000000000000000000000000000000002−22−22−22−2
χ322222-2-2-2-222-2-2222222-2-222-2-2-2-2-2-22-22-2000000000000002-22-200000000000000000000000000000000−22−22−22−22
χ332222-2-2-2-222-2-2222222-2-222-2-2-2-2-2-2-22-2200000000000000-22-22000000000000000000000000000000002−22−2−22−22
χ342222-2-2-2-222-2-2222222-2-222-2-2-2-2-2-2-22-2200000000000000-22-2200000000000000000000000000000000−22−222−22−2
χ3522-2-222-2-22-2-222222-2-2-2-2-2-2-2-2222222-2-2-2-222-220000000022-2-2-2-22200000000-2-222000000000000000000000000
χ3622-2-222-2-22-2-222222-2-2-2-2-2-2-2-22222-2-222-2-2222-200000000-2-22222-2-200000000-2-222000000000000000000000000
χ3722-2-222-2-22-2-22-1-1-1-111111111-1-1-1-122-2-222-2-22-222-2-222-2-2-1-111-1-111-1-1-1-11111-1-111-1-1-1-111110000000000000000
χ3822-2-222-2-22-2-22-1-1-1-111111111-1-1-1-122-2-222-2-22-2-2-222-2-222-1-111-1-1111111-1-1-1-1-1-1111111-1-1-1-10000000000000000
χ3922-2-222-2-22-2-22-1-1-1-111111111-1-1-1-122-2-2-2-222-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i311-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ4022-2-222-2-22-2-22-1-1-1-111111111-1-1-1-122-2-2-2-222-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i311-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ4122-2-222-2-22-2-22-1-1-1-111111111-1-1-1-1-2-22222-2-2-2222-2-2-2-22211-1-111-1-11111-1-1-1-1-1-111-1-1-1-111110000000000000000
χ4222-2-222-2-22-2-22-1-1-1-111111111-1-1-1-1-2-22222-2-2-22-2-22222-2-211-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-10000000000000000
χ4322-2-222-2-22-2-22-1-1-1-111111111-1-1-1-1-2-222-2-2222-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i311-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ4422-2-222-2-22-2-22-1-1-1-111111111-1-1-1-1-2-222-2-2222-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i311-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ4522-2-222-2-2-222-222-2-2-2-2-2-222222-2-2200002-2-22000000000000000000000000002-2-220000000000002i−2i−2i2i00000000
χ4622-2-222-2-2-222-222-2-2-2-2-2-222222-2-2200002-2-22000000000000000000000000002-2-22000000000000−2i2i2i−2i00000000
χ4722-2-222-2-2-222-222-2-2-2-2-2-222222-2-220000-222-200000000000000000000000000-222-2000000002i−2i−2i2i000000000000
χ4822-2-222-2-2-222-222-2-2-2-2-2-222222-2-220000-222-200000000000000000000000000-222-200000000−2i2i2i−2i000000000000
χ4922-2-2-2-2222-22-22222-2-222-2-222-2-2-2-22-2-22000000000000002-2-2200000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ5022-2-2-2-2222-22-22222-2-222-2-222-2-2-2-22-2-22000000000000002-2-2200000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ5122-2-2-2-2222-22-22222-2-222-2-222-2-2-2-2-222-200000000000000-222-200000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ5222-2-2-2-2222-22-22222-2-222-2-222-2-2-2-2-222-200000000000000-222-200000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ5344444444-4-4-4-4-2-222-2-2-2-22222-222-200004-44-400000000000000000000000000-22-22000000000000000000000000
χ5444444444-4-4-4-4-2-222-2-2-2-22222-222-20000-44-44000000000000000000000000002-22-2000000000000000000000000
χ554444-4-4-4-444-4-4-2-2-2-2-2-222-2-22222224-44-400000000000000-22-220000000000000000000000000000000000000000
χ564444-4-4-4-444-4-4-2-2-2-2-2-222-2-2222222-44-44000000000000002-22-20000000000000000000000000000000000000000
χ574444-4-4-4-4-4-44444-4-444-4-4-4-444-444-400000000000000000000000000000000000000000000000000000000000000
χ584444-4-4-4-4-4-444-2-222-2-22222-2-22-2-22000000000000000000000023−2323−23000000000000000000000000000000000000
χ594444-4-4-4-4-4-444-2-222-2-22222-2-22-2-220000000000000000000000−2323−2323000000000000000000000000000000000000
χ6044-4-444-4-4-444-4-2-2222222-2-2-2-2-222-200004-4-4400000000000000000000000000-222-2000000000000000000000000
χ6144-4-444-4-4-444-4-2-2222222-2-2-2-2-222-20000-444-4000000000000000000000000002-2-22000000000000000000000000
χ6244-4-4-4-4444-44-4-2-2-2-222-2-222-2-222224-4-4400000000000000-222-20000000000000000000000000000000000000000
χ6344-4-4-4-4444-44-4-2-2-2-222-2-222-2-22222-444-4000000000000002-2-220000000000000000000000000000000000000000
χ6444-4-4-4-444-44-4444-4-4-4-44444-4-4-444-400000000000000000000000000000000000000000000000000000000000000
χ6544-4-4-4-444-44-44-2-22222-2-2-2-2222-2-22000000000000000000000023−23−2323000000000000000000000000000000000000
χ6644-4-4-4-444-44-44-2-22222-2-2-2-2222-2-220000000000000000000000−232323−23000000000000000000000000000000000000
χ674-44-44-44-400004-4004-44-40000400-4000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ684-44-44-44-400004-4004-44-40000400-400000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ694-44-44-44-40000-22−2i32i3-22-22−2i32i3−2i32i3-2−2i32i32000000000000002i−2i2i−2i000000002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ220000000000000000000000000000
χ704-44-44-44-40000-22−2i32i3-22-22−2i32i3−2i32i3-2−2i32i3200000000000000−2i2i−2i2i00000000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ220000000000000000000000000000
χ714-44-44-44-40000-222i3−2i3-22-222i3−2i32i3−2i3-22i3−2i32000000000000002i−2i2i−2i000000002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ140000000000000000000000000000
χ724-44-44-44-40000-222i3−2i3-22-222i3−2i32i3−2i3-22i3−2i3200000000000000−2i2i−2i2i00000000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ140000000000000000000000000000
χ734-44-4-44-4400004-4004-4-440000-400400000000002-22-20000000000000000000000002-22-22-22-20000000000000000
χ744-44-4-44-4400004-4004-4-440000-40040000000000-22-22000000000000000000000000-22-22-22-220000000000000000
χ754-44-4-44-440000-22−2i32i3-222-2−2i32i32i3−2i322i3−2i3-200000000002-22-2000000000000000000000000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000
χ764-44-4-44-440000-22−2i32i3-222-2−2i32i32i3−2i322i3−2i3-20000000000-22-220000000000000000000000001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000
χ774-44-4-44-440000-222i3−2i3-222-22i3−2i3−2i32i32−2i32i3-200000000002-22-2000000000000000000000000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000
χ784-44-4-44-440000-222i3−2i3-222-22i3−2i3−2i32i32−2i32i3-20000000000-22-220000000000000000000000001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000
χ794-4-444-4-4400004-400-44-440000400-4000000000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ804-4-444-4-4400004-400-44-440000400-400000000000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ814-4-444-4-440000-22−2i32i32-22-22i3−2i32i3−2i3-2−2i32i32000000000000002i−2i−2i2i000000002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ220000000000000000000000000000
χ824-4-444-4-440000-22−2i32i32-22-22i3−2i32i3−2i3-2−2i32i3200000000000000−2i2i2i−2i00000000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ220000000000000000000000000000
χ834-4-444-4-440000-222i3−2i32-22-2−2i32i3−2i32i3-22i3−2i32000000000000002i−2i−2i2i000000002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ140000000000000000000000000000
χ844-4-444-4-440000-222i3−2i32-22-2−2i32i3−2i32i3-22i3−2i3200000000000000−2i2i2i−2i00000000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ140000000000000000000000000000
χ854-4-44-444-400004-400-444-40000-400400000000002-2-220000000000000000000000002-22-2-22-220000000000000000
χ864-4-44-444-400004-400-444-40000-40040000000000-222-2000000000000000000000000-22-222-22-20000000000000000
χ874-4-44-444-40000-22−2i32i32-2-222i3−2i3−2i32i322i3−2i3-200000000002-2-22000000000000000000000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i30000000000000000
χ884-4-44-444-40000-22−2i32i32-2-222i3−2i3−2i32i322i3−2i3-20000000000-222-20000000000000000000000001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i30000000000000000
χ894-4-44-444-40000-222i3−2i32-2-22−2i32i32i3−2i32−2i32i3-200000000002-2-22000000000000000000000000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i30000000000000000
χ904-4-44-444-40000-222i3−2i32-2-22−2i32i32i3−2i32−2i32i3-20000000000-222-20000000000000000000000001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i30000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.