Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×Dic121 |
| unambiguous semidirect product | C121⋊(C4×C72) |
| derived, Sylow | C121 ⋊ C4×C72 |
| Hall | C72×C121 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | D121 |
| commutator, hypocenter | C121 | C4×C72 |
| Frattini | C2×C11 | C72×D11 |
| Fitting | C2×C72×C121 | C2 |
| socle, prime radical | C2×C72×C11 | D11 |
| cosocle | C2×C121 | C2×C72 |
| LCS | G ▷ C121 | |
| UCS | C1 ◁ C2×C72 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23716 |
6076 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 11);