Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C112 · Schur multiplier (H2) = C11 |
| direct product | C7×C112×Dic7 |
| unambiguous semidirect product | C7⋊(C4×C7×C112) |
| derived | C7 ⋊ C4×C7×C112 |
| Hall | C72×C112 ⋊ C4 |
| Sylow | C72 ⋊ C4×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C112 | D7 |
| commutator, hypocenter | C7 | C4×C7×C112 |
| Frattini | C2 | C7×C112×D7 |
| Fitting, socle, prime radical | C2×C72×C112 | C2 |
| cosocle | C2×C7 | C2×C7×C112 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C7×C112 | |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3388 |
8470 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 54);