Finite Group DatabasebetaFinite Group Databasebeta| order | 13524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D161⋊D21 |
| Fitting, socle, derived, Hall | C3×C72×C23 ⋊ C22 |
| Hall | C72×C23 ⋊ C2×D3 |
| Hall | C3×C72 ⋊ C2×D23 |
| Hall | C3×C23 ⋊ D72 |
| Sylow | C72 ⋊ D3×D23 |
| Sylow | C23 ⋊ D7×D21 |
| Sylow | C3 ⋊ (C7⋊D7)⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C72×C23 | C22 |
| LCS | G ▷ C3×C72×C23 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| transitive degree | μt(G) = 966 |
A minimal faithful permutation representation — 2 generators on 40 points:
(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(25,26)(27,28)(29,30)(31,32)(35,36)(37,38)(39,40);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25,26)(28,29)(30,31)(32,33)(34,35,37,39,40,38,36)Polycyclic presentation:
2^2,3,7^2,23|d^a=d^6,f^a=f^22,c^b=c^2,d^b=d^6,e^b=e^6885 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13524, 135);