Finite Group Databasebeta

← Group #10713686

Character table — Group #10713686

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order124422234446668888888812121212444466888812121212121212121212242424242424242424242424242424242244666612121212444488881616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-111111111-1-1-1-1
χ911-1-1-11-11-1111111111-1-1-1-1-1-1-1-111-1-1-1-11-11-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-1-11-11-1111111111-1-1-1-1-1-1-1-111-1-1-1-11-11-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-1-11-11-1111111111-1-1-1-1-1-1-1-111-1-1-1-11-11-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-1-11-11-1111111111-1-1-1-1-1-1-1-111-1-1-1-11-11-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-1-11-11-11111111-1-111-1-1-1-1-1-1-1-111-1-11-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411-1-1-11-11-11111111-1-111-1-1-1-1-1-1-1-111-1-11-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511-1-1-11-11-11111111-1-111-1-1-1-1-1-1-1-111-1-11-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611-1-1-11-11-11111111-1-111-1-1-1-1-1-1-1-111-1-11-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-22222-2-22222-2-2-2-222-2-222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ192222222-1222-1-1-122222222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ202222222-1222-1-1-122222222-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ212222222-1222-1-1-122-2-2-2-222-1-1-1-1-2-2-2-2-1-122-2-211111111-1-1-1-1-1-1-1-1-1-1111111112-22-2-1-111-1-1110000000000000000
χ222222222-1222-1-1-122-2-2-2-222-1-1-1-1-2-2-2-2-1-122-2-211111111-1-1-1-1-1-1-1-1-1-111111111-22-2211-1-111-1-10000000000000000
χ232222222-1222-1-1-1-2-22222-2-2-1-1-1-1-2-2-2-2-1-1-2-22211111111-1-111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3−i3i3−i3i30000000000000000
χ242222222-1222-1-1-1-2-22222-2-2-1-1-1-1-2-2-2-2-1-1-2-22211111111-1-111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3i3−i3i3−i30000000000000000
χ252222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ262222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ2722222-2-22-22-2-2-222200002222-2-200002-2-2-200000000002-222-2-222-2-20000000000000000000000002-22-200000000
χ2822222-2-22-22-2-2-222200002222-2-200002-2-2-200000000002-222-2-222-2-2000000000000000000000000-22-2200000000
χ2922222-2-22-22-2-2-22-2-20000-2-222-2-200002-22200000000002-2-2-222-2-222000000000000000000002i−2i2i−2i000000000000
χ3022222-2-22-22-2-2-22-2-20000-2-222-2-200002-22200000000002-2-2-222-2-22200000000000000000000−2i2i−2i2i000000000000
χ312222-2-222-2-22-2-220022220022-2-20000-2200-2-200000000-220000000022-2-222-2-2000000000000000000002−22−22−22−2
χ322222-2-222-2-22-2-220022220022-2-20000-2200-2-200000000-220000000022-2-222-2-200000000000000000000−22−22−22−22
χ332222-2-222-2-22-2-2200-2-2-2-20022-2-20000-22002200000000-2200000000-2-222-2-222000000000000000000002−22−2−22−22
χ342222-2-222-2-22-2-2200-2-2-2-20022-2-20000-22002200000000-2200000000-2-222-2-22200000000000000000000−22−222−22−2
χ3522-2-22-2-222-22-2-220022-2-200-2-22200002-200-2200000000-220000000022-2-2-2-22200000000000000000000−i2i2i2−i2−i2i2i2−i2
χ3622-2-22-2-222-22-2-220022-2-200-2-22200002-200-2200000000-220000000022-2-2-2-22200000000000000000000i2−i2−i2i2i2−i2−i2i2
χ3722-2-22-2-222-22-2-2200-2-22200-2-22200002-2002-200000000-2200000000-2-22222-2-200000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3822-2-22-2-222-22-2-2200-2-22200-2-22200002-2002-200000000-2200000000-2-22222-2-200000000000000000000i2−i2−i2i2−i2i2i2−i2
χ3922-2-2-22-22-222222-2-222-2-222-2-2-2-2-2-222-2-2-222-2-2-2-2-2222222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ4022-2-2-22-22-222222-2-2-2-22222-2-2-2-222-2-2-2-2-22-222222-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ4122-2-2-22-2-1-222-1-1-12222-2-2-2-2111122-2-2112-22-2-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111122-2-2-1-1-1-111110000000000000000
χ4222-2-2-22-2-1-222-1-1-12222-2-2-2-2111122-2-2112-22-2-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-2-2221111-1-1-1-10000000000000000
χ4322-2-2-22-2-1-222-1-1-122-2-222-2-21111-2-222112-2-221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ4422-2-2-22-2-1-222-1-1-122-2-222-2-21111-2-222112-2-221111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ4522-2-2-22-2-1-222-1-1-1-2-222-2-2221111-2-22211-222-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ4622-2-2-22-2-1-222-1-1-1-2-222-2-2221111-2-22211-222-21111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ4722-2-2-22-2-1-222-1-1-1-2-2-2-22222111122-2-211-22-22-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ4822-2-2-22-2-1-222-1-1-1-2-2-2-22222111122-2-211-22-22-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ4922-2-2-2-22222-2-2-22220000-2-2-2-2220000-22-2200000000002-222-2-2-2-2220000000000000000000000002i−2i−2i2i00000000
χ5022-2-2-2-22222-2-2-22220000-2-2-2-2220000-22-2200000000002-222-2-2-2-222000000000000000000000000−2i2i2i−2i00000000
χ5122-2-2-2-22222-2-2-22-2-2000022-2-2220000-222-200000000002-2-2-22222-2-2000000000000000000002-2-22000000000000
χ5222-2-2-2-22222-2-2-22-2-2000022-2-2220000-222-200000000002-2-2-22222-2-200000000000000000000-222-2000000000000
χ5344444-4-4-2-44-422-244000044-2-2220000-22-4-40000000000-22-2-222-2-222000000000000000000000000000000000000
χ5444444-4-4-2-44-422-2-4-40000-4-4-2-2220000-22440000000000-2222-2-222-2-2000000000000000000000000000000000000
χ554444-44-444-4-44440000000044440000-4-4000000000000-4-400000000000000000000000000000000000000000000
χ564444-44-4-24-4-4-2-2-200000000-2-2-2-20000220000−2i3−2i32i32i3−2i3−2i32i32i32200000000000000000000000000000000000000000000
χ574444-44-4-24-4-4-2-2-200000000-2-2-2-200002200002i32i3−2i3−2i32i32i3−2i3−2i32200000000000000000000000000000000000000000000
χ584444-4-44-2-4-4422-200444400-2-22200002-200-4-4000000002-200000000-2-222-2-2220000000000000000000000000000
χ594444-4-44-2-4-4422-200-4-4-4-400-2-22200002-20044000000002-20000000022-2-222-2-20000000000000000000000000000
χ6044-4-44444-4-4-444400000000-4-4-4-4000044000000000000-4-400000000000000000000000000000000000000000000
χ6144-4-4444-2-4-4-4-2-2-20000000022220000-2-20000−2i3−2i32i32i32i32i3−2i3−2i32200000000000000000000000000000000000000000000
χ6244-4-4444-2-4-4-4-2-2-20000000022220000-2-200002i32i3−2i3−2i3−2i3−2i32i32i32200000000000000000000000000000000000000000000
χ6344-4-44-4-4-24-4422-20044-4-40022-2-20000-2200-44000000002-200000000-2-22222-2-20000000000000000000000000000
χ6444-4-44-4-4-24-4422-200-4-4440022-2-20000-22004-4000000002-20000000022-2-2-2-2220000000000000000000000000000
χ6544-4-4-4-44-244-422-2440000-4-422-2-200002-2-440000000000-22-2-22222-2-2000000000000000000000000000000000000
χ6644-4-4-4-44-244-422-2-4-400004422-2-200002-24-40000000000-2222-2-2-2-222000000000000000000000000000000000000
χ674-44i−4i000400000-422−2222−22−2i22i2−2i22i24i−4i002-22i−2i0000002-22-22i−2i2i−2i0022−2200−2i22i20022−2200−2i22i2000000000000000000000000000000
χ684-44i−4i000400000-422−22−22222i2−2i2−2i22i24i−4i00-22−2i2i000000-22-22−2i2i−2i2i0022−2200−2i22i200−2222002i2−2i2000000000000000000000000000000
χ694-44i−4i000400000-4−222222−22−2i22i22i2−2i24i−4i00-22−2i2i000000-22-22−2i2i−2i2i00−2222002i2−2i20022−2200−2i22i2000000000000000000000000000000
χ704-44i−4i000400000-4−2222−22222i2−2i22i2−2i24i−4i002-22i−2i0000002-22-22i−2i2i−2i00−2222002i2−2i200−2222002i2−2i2000000000000000000000000000000
χ714-44i−4i000-2000−2i32i3222−2222−22−2i22i2−2i22i2−2i2i23−232-22i−2i000000−1−i31+i3−1+i31−i32ζ22−2ζ222ζ14−2ζ1400−22i6−i6i2−i26−6−22i6−i6i2−i26−60000000000000000000000000000
χ724-44i−4i000-2000−2i32i3222−22−22222i2−2i2−2i22i2−2i2i23−23-22−2i2i0000001+i3−1−i31−i3−1+i3−2ζ222ζ22−2ζ142ζ1400−22i6−i6i2−i26−62−2−i6i6−i2i2−660000000000000000000000000000
χ734-44i−4i000-2000−2i32i32−222222−22−2i22i22i2−2i2−2i2i23−23-22−2i2i0000001+i3−1−i31−i3−1+i3−2ζ222ζ22−2ζ142ζ14002−2−i6i6−i2i2−66−22i6−i6i2−i26−60000000000000000000000000000
χ744-44i−4i000-2000−2i32i32−2222−22222i2−2i22i2−2i2−2i2i23−232-22i−2i000000−1−i31+i3−1+i31−i32ζ22−2ζ222ζ14−2ζ14002−2−i6i6−i2i2−662−2−i6i6−i2i2−660000000000000000000000000000
χ754-44i−4i000-20002i3−2i3222−2222−22−2i22i2−2i22i2−2i2i−23232-22i−2i000000−1+i31−i3−1−i31+i32ζ14−2ζ142ζ22−2ζ2200−22−i6i6i2−i2−66−22−i6i6i2−i2−660000000000000000000000000000
χ764-44i−4i000-20002i3−2i3222−22−22222i2−2i2−2i22i2−2i2i−2323-22−2i2i0000001−i3−1+i31+i3−1−i3−2ζ142ζ14−2ζ222ζ2200−22−i6i6i2−i2−662−2i6−i6−i2i26−60000000000000000000000000000
χ774-44i−4i000-20002i3−2i32−222222−22−2i22i22i2−2i2−2i2i−2323-22−2i2i0000001−i3−1+i31+i3−1−i3−2ζ142ζ14−2ζ222ζ22002−2i6−i6−i2i26−6−22−i6i6i2−i2−660000000000000000000000000000
χ784-44i−4i000-20002i3−2i32−2222−22222i2−2i22i2−2i2−2i2i−23232-22i−2i000000−1+i31−i3−1−i31+i32ζ14−2ζ142ζ22−2ζ22002−2i6−i6−i2i26−62−2i6−i6−i2i26−60000000000000000000000000000
χ794-4−4i4i000400000-422−2222−222i2−2i22i2−2i2−4i4i002-2−2i2i0000002-22-2−2i2i−2i2i0022−22002i2−2i20022−22002i2−2i2000000000000000000000000000000
χ804-4−4i4i000400000-422−22−2222−2i22i22i2−2i2−4i4i00-222i−2i000000-22-222i−2i2i−2i0022−22002i2−2i200−222200−2i22i2000000000000000000000000000000
χ814-4−4i4i000400000-4−222222−222i2−2i2−2i22i2−4i4i00-222i−2i000000-22-222i−2i2i−2i00−222200−2i22i20022−22002i2−2i2000000000000000000000000000000
χ824-4−4i4i000400000-4−2222−2222−2i22i2−2i22i2−4i4i002-2−2i2i0000002-22-2−2i2i−2i2i00−222200−2i22i200−222200−2i22i2000000000000000000000000000000
χ834-4−4i4i000-2000−2i32i3222−2222−222i2−2i22i2−2i22i−2i−23232-2−2i2i000000−1−i31+i3−1+i31−i3−2ζ222ζ22−2ζ142ζ1400−22i6−i6−i2i2−66−22i6−i6−i2i2−660000000000000000000000000000
χ844-4−4i4i000-2000−2i32i3222−22−2222−2i22i22i2−2i22i−2i−2323-222i−2i0000001+i3−1−i31−i3−1+i32ζ22−2ζ222ζ14−2ζ1400−22i6−i6−i2i2−662−2−i6i6i2−i26−60000000000000000000000000000
χ854-4−4i4i000-2000−2i32i32−222222−222i2−2i2−2i22i22i−2i−2323-222i−2i0000001+i3−1−i31−i3−1+i32ζ22−2ζ222ζ14−2ζ14002−2−i6i6i2−i26−6−22i6−i6−i2i2−660000000000000000000000000000
χ864-4−4i4i000-2000−2i32i32−2222−2222−2i22i2−2i22i22i−2i−23232-2−2i2i000000−1−i31+i3−1+i31−i3−2ζ222ζ22−2ζ142ζ14002−2−i6i6i2−i26−62−2−i6i6i2−i26−60000000000000000000000000000
χ874-4−4i4i000-20002i3−2i3222−2222−222i2−2i22i2−2i22i−2i23−232-2−2i2i000000−1+i31−i3−1−i31+i3−2ζ142ζ14−2ζ222ζ2200−22−i6i6−i2i26−6−22−i6i6−i2i26−60000000000000000000000000000
χ884-4−4i4i000-20002i3−2i3222−22−2222−2i22i22i2−2i22i−2i23−23-222i−2i0000001−i3−1+i31+i3−1−i32ζ14−2ζ142ζ22−2ζ2200−22−i6i6−i2i26−62−2i6−i6i2−i2−660000000000000000000000000000
χ894-4−4i4i000-20002i3−2i32−222222−222i2−2i2−2i22i22i−2i23−23-222i−2i0000001−i3−1+i31+i3−1−i32ζ14−2ζ142ζ22−2ζ22002−2i6−i6i2−i2−66−22−i6i6−i2i26−60000000000000000000000000000
χ904-4−4i4i000-20002i3−2i32−2222−2222−2i22i2−2i22i22i−2i23−232-2−2i2i000000−1+i31−i3−1−i31+i3−2ζ142ζ14−2ζ222ζ22002−2i6−i6i2−i2−662−2i6−i6i2−i2−660000000000000000000000000000

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