Finite Group Databasebeta

← Group #10713692

Character table — Group #10713692

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order1222223444466666668888888844448888121212121212121212121212242424242424242424242424242424242244666612121212444488881616161616161616
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
χ511111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911-1-1-111-111-1-1-1-1-11111111-1-1-1-111-1-11-11-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-1-111-111-1-1-1-1-11111111-1-1-1-111-1-11-11-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-1-111-111-1-1-1-1-11111111-1-1-1-111-1-11-11-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-1-111-111-1-1-1-1-11111111-1-1-1-111-1-11-11-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-1-111-111-1-1-1-1-111111-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411-1-1-111-111-1-1-1-1-111111-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511-1-1-111-111-1-1-1-1-111111-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611-1-1-111-111-1-1-1-1-111111-1-111-1-1-1-1111-1-11-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ19222222-12222-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ20222222-12222-1-1-1-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ21222222-12222-1-1-1-1-1-1-122-2-2-2-222-2-2-2-222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ22222222-12222-1-1-1-1-1-1-122-2-2-2-222-2-2-2-222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ23222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-2-22211111111-1-1-1-111111111-1-1-1-1-1-1-1-10000−i3i3−i3i3−i3i3−i3i30000000000000000
χ24222222-12222-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-2-22211111111-1-1-1-111111111-1-1-1-1-1-1-1-10000i3−i3i3−i3i3−i3i3−i30000000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ272222-2-2222-2-222-2-2-2-22220000220000-2-200000000002-22-222-2-222-2-2000000000000000000002-22-2000000000000
χ282222-2-2222-2-222-2-2-2-22220000220000-2-200000000002-22-222-2-222-2-200000000000000000000-22-22000000000000
χ292222-2-2222-2-222-2-2-2-22-2-20000-2-200002200000000002-22-2-2-222-2-2220000000000000000000000002i−2i2i−2i00000000
χ302222-2-2222-2-222-2-2-2-22-2-20000-2-200002200000000002-22-2-2-222-2-222000000000000000000000000−2i2i−2i2i00000000
χ312222-2-22-2-22222-2-2-2-2200222200000000-2-200000000-22-220000000022-2-222-2-2000000000000000000002−22−22−22−2
χ322222-2-22-2-22222-2-2-2-2200222200000000-2-200000000-22-220000000022-2-222-2-200000000000000000000−22−22−22−22
χ332222-2-22-2-22222-2-2-2-2200-2-2-2-2000000002200000000-22-2200000000-2-222-2-222000000000000000000002−22−2−22−22
χ342222-2-22-2-22222-2-2-2-2200-2-2-2-2000000002200000000-22-2200000000-2-222-2-22200000000000000000000−22−222−22−2
χ3522-2-22-222-22-2-2-222-2-220022-2-200000000-22000000002-2-220000000022-2-2-2-22200000000000000000000−i2i2i2−i2−i2i2i2−i2
χ3622-2-22-222-22-2-2-222-2-220022-2-200000000-22000000002-2-220000000022-2-2-2-22200000000000000000000i2−i2−i2i2i2−i2−i2i2
χ3722-2-22-222-22-2-2-222-2-2200-2-222000000002-2000000002-2-2200000000-2-22222-2-200000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3822-2-22-222-22-2-2-222-2-2200-2-222000000002-2000000002-2-2200000000-2-22222-2-200000000000000000000i2−i2−i2i2−i2i2i2−i2
χ3922-2-22-22-22-22-2-222-2-22220000-2-20000-220000000000-222-222-2-2-2-222000000000000000000002i−2i−2i2i000000000000
χ4022-2-22-22-22-22-2-222-2-22220000-2-20000-220000000000-222-222-2-2-2-22200000000000000000000−2i2i2i−2i000000000000
χ4122-2-22-22-22-22-2-222-2-22-2-200002200002-20000000000-222-2-2-22222-2-20000000000000000000000002-2-2200000000
χ4222-2-22-22-22-22-2-222-2-22-2-200002200002-20000000000-222-2-2-22222-2-2000000000000000000000000-222-200000000
χ4322-2-2-222-222-2-2-2-2-2222-2-222-2-222-2-222-222-2-2-2-2-22222-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ4422-2-2-222-222-2-2-2-2-2222-2-2-2-2222222-2-2-22-222222-2-2-2-2-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ4522-2-2-22-1-222-21111-1-1-12222-2-2-2-222-2-22-22-2-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111112-22-2-1-111-1-1110000000000000000
χ4622-2-2-22-1-222-21111-1-1-12222-2-2-2-222-2-22-22-2-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-22-2211-1-111-1-10000000000000000
χ4722-2-2-22-1-222-21111-1-1-122-2-222-2-2-2-2222-2-221111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ4822-2-2-22-1-222-21111-1-1-122-2-222-2-2-2-2222-2-221111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ4922-2-2-22-1-222-21111-1-1-1-2-222-2-222-2-222-222-21111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ5022-2-2-22-1-222-21111-1-1-1-2-222-2-222-2-222-222-21111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ5122-2-2-22-1-222-21111-1-1-1-2-2-2-2222222-2-2-22-22-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ5222-2-2-22-1-222-21111-1-1-1-2-2-2-2222222-2-2-22-22-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ534444444-4-4-4-44444444000000000000000000000000-4-4-4-400000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-2-2-2-20000000000000000−2i3−2i32i32i3−2i3−2i32i32i3222200000000000000000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-2-2-2-2-200000000000000002i32i3−2i3−2i32i32i3−2i3−2i3222200000000000000000000000000000000000000000000
χ564444-4-4-244-4-4-2-22222-2440000440000-4-40000000000-22-22-2-222-2-222000000000000000000000000000000000000
χ574444-4-4-244-4-4-2-22222-2-4-40000-4-40000440000000000-22-2222-2-222-2-2000000000000000000000000000000000000
χ584444-4-4-2-4-444-2-22222-200444400000000-4-4000000002-22-200000000-2-222-2-2220000000000000000000000000000
χ594444-4-4-2-4-444-2-22222-200-4-4-4-40000000044000000002-22-20000000022-2-222-2-20000000000000000000000000000
χ6044-4-44-4-24-44-422-2-222-20044-4-400000000-4400000000-222-200000000-2-22222-2-20000000000000000000000000000
χ6144-4-44-4-24-44-422-2-222-200-4-444000000004-400000000-222-20000000022-2-2-2-2220000000000000000000000000000
χ6244-4-44-4-2-44-4422-2-222-2440000-4-40000-4400000000002-2-22-2-22222-2-2000000000000000000000000000000000000
χ6344-4-44-4-2-44-4422-2-222-2-4-400004400004-400000000002-2-2222-2-2-2-222000000000000000000000000000000000000
χ6444-4-4-4444-4-44-4-4-4-444400000000000000000000000044-4-400000000000000000000000000000000000000000000
χ6544-4-4-44-24-4-442222-2-2-20000000000000000−2i3−2i32i32i32i32i3−2i3−2i3-2-22200000000000000000000000000000000000000000000
χ6644-4-4-44-24-4-442222-2-2-200000000000000002i32i3−2i3−2i3−2i3−2i32i32i3-2-22200000000000000000000000000000000000000000000
χ674-44-400400004-40000-422−22−2i22i2−2i22i222−222i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i000022−220022−2200−2i22i200−2i22i2000000000000000000000000000000
χ684-44-400400004-40000-422−222i2−2i22i2−2i222−22−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000022−220022−22002i2−2i2002i2−2i2000000000000000000000000000000
χ694-44-400400004-40000-4−2222−2i22i2−2i22i2−2222−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i0000−222200−222200−2i22i200−2i22i2000000000000000000000000000000
χ704-44-400400004-40000-4−22222i2−2i22i2−2i2−22222i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i0000−222200−2222002i2−2i2002i2−2i2000000000000000000000000000000
χ714-44-400-20000-22−2i32i3−2i32i3222−22−2i22i2−2i22i222−222i−2i2i−2i00002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ220000−22i6−i6−22i6−i6i2−i26−6i2−i26−60000000000000000000000000000
χ724-44-400-20000-22−2i32i3−2i32i3222−222i2−2i22i2−2i222−22−2i2i−2i2i0000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ220000−22i6−i6−22i6−i6−i2i2−66−i2i2−660000000000000000000000000000
χ734-44-400-20000-22−2i32i3−2i32i32−2222−2i22i2−2i22i2−2222−2i2i−2i2i0000−2ζ142ζ14−2ζ222ζ22−2ζ142ζ14−2ζ222ζ2200002−2−i6i62−2−i6i6i2−i26−6i2−i26−60000000000000000000000000000
χ744-44-400-20000-22−2i32i3−2i32i32−22222i2−2i22i2−2i2−22222i−2i2i−2i00002ζ14−2ζ142ζ22−2ζ222ζ14−2ζ142ζ22−2ζ2200002−2−i6i62−2−i6i6−i2i2−66−i2i2−660000000000000000000000000000
χ754-44-400-20000-222i3−2i32i3−2i3222−22−2i22i2−2i22i222−222i−2i2i−2i00002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ140000−22−i6i6−22−i6i6i2−i2−66i2−i2−660000000000000000000000000000
χ764-44-400-20000-222i3−2i32i3−2i3222−222i2−2i22i2−2i222−22−2i2i−2i2i0000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ140000−22−i6i6−22−i6i6−i2i26−6−i2i26−60000000000000000000000000000
χ774-44-400-20000-222i3−2i32i3−2i32−2222−2i22i2−2i22i2−2222−2i2i−2i2i0000−2ζ222ζ22−2ζ142ζ14−2ζ222ζ22−2ζ142ζ1400002−2i6−i62−2i6−i6i2−i2−66i2−i2−660000000000000000000000000000
χ784-44-400-20000-222i3−2i32i3−2i32−22222i2−2i22i2−2i2−22222i−2i2i−2i00002ζ22−2ζ222ζ14−2ζ142ζ22−2ζ222ζ14−2ζ1400002−2i6−i62−2i6−i6−i2i26−6−i2i26−60000000000000000000000000000
χ794-4-440040000-440000-422−22−2i22i22i2−2i2−22222i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i000022−2200−222200−2i22i2002i2−2i2000000000000000000000000000000
χ804-4-440040000-440000-422−222i2−2i2−2i22i2−2222−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i000022−2200−2222002i2−2i200−2i22i2000000000000000000000000000000
χ814-4-440040000-440000-4−2222−2i22i22i2−2i222−22−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i0000−22220022−2200−2i22i2002i2−2i2000000000000000000000000000000
χ824-4-440040000-440000-4−22222i2−2i2−2i22i222−222i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i0000−22220022−22002i2−2i200−2i22i2000000000000000000000000000000
χ834-4-4400-200002-2−2i32i32i3−2i3222−22−2i22i22i2−2i2−22222i−2i−2i2i00002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ140000−22−i6i62−2i6−i6i2−i2−66−i2i26−60000000000000000000000000000
χ844-4-4400-200002-2−2i32i32i3−2i3222−222i2−2i2−2i22i2−2222−2i2i2i−2i0000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ140000−22−i6i62−2i6−i6−i2i26−6i2−i2−660000000000000000000000000000
χ854-4-4400-200002-2−2i32i32i3−2i32−2222−2i22i22i2−2i222−22−2i2i2i−2i0000−2ζ222ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ1400002−2i6−i6−22−i6i6i2−i2−66−i2i26−60000000000000000000000000000
χ864-4-4400-200002-2−2i32i32i3−2i32−22222i2−2i2−2i22i222−222i−2i−2i2i00002ζ22−2ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ1400002−2i6−i6−22−i6i6−i2i26−6i2−i2−660000000000000000000000000000
χ874-4-4400-200002-22i3−2i3−2i32i3222−22−2i22i22i2−2i2−22222i−2i−2i2i00002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ220000−22i6−i62−2−i6i6i2−i26−6−i2i2−660000000000000000000000000000
χ884-4-4400-200002-22i3−2i3−2i32i3222−222i2−2i2−2i22i2−2222−2i2i2i−2i0000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ220000−22i6−i62−2−i6i6−i2i2−66i2−i26−60000000000000000000000000000
χ894-4-4400-200002-22i3−2i3−2i32i32−2222−2i22i22i2−2i222−22−2i2i2i−2i0000−2ζ142ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ2200002−2−i6i6−22i6−i6i2−i26−6−i2i2−660000000000000000000000000000
χ904-4-4400-200002-22i3−2i3−2i32i32−22222i2−2i2−2i22i222−222i−2i−2i2i00002ζ14−2ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ2200002−2−i6i6−22i6−i6−i2i2−66i2−i26−60000000000000000000000000000

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