Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C11⋊D11)⋊D49 |
| unambiguous semidirect product | D539⋊D11 |
| Fitting, derived, Hall | C112×C49 ⋊ C22 |
| Sylow | C112 ⋊ C2×D49 |
| Sylow | C49 ⋊ D112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C112×C49 | C22 |
| Frattini | C7 | D77⋊D11 |
| socle | C7×C112 | C2×D7 |
| LCS | G ▷ C112×C49 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1078 |
Polycyclic presentation:
2^2,7,11^2,7|c^7=f^6,c^a=c^6f,d^a=d^10,f^a=f^6,d^b=d^10,e^b=e^101537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 41);