Finite Group DatabasebetaFinite Group Databasebeta| order | 23716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C121 · Schur multiplier (H2) = C2 |
| direct product | D72×C121 |
| unambiguous semidirect product | (C7×D7)⋊(C2×C121) |
| unambiguous semidirect product | (C7⋊D7)⋊(C2×C121) |
| Fitting, Hall | C72×C121 ⋊ C22 |
| derived, Sylow | C72 ⋊ C22×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | D72 |
| commutator, hypocenter | C72 | C22×C121 |
| Frattini | C11 | C11×D72 |
| Fitting | C72×C121 | C22 |
| socle, cosocle | C72×C11 | C22×C11 |
| prime radical | C11×D72 | C11 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C121 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1694 |
3025 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23716, 25);