Finite Group DatabasebetaFinite Group Databasebeta| order | 24892 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C72 · Schur multiplier (H2) = C7 |
| direct product | C7×Dic127⋊C7 |
| unambiguous semidirect product | Dic127⋊C72 |
| unambiguous semidirect product | (C127⋊C7)⋊(C4×C7) |
| unambiguous semidirect product | (C7×Dic127)⋊C7 |
| derived, Sylow | C127 ⋊ C4×C72 |
| Hall | C7×C127⋊C7 ⋊ C4 |
| Hall | Dic127 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D127⋊C7 |
| commutator, hypocenter | C127 | C4×C72 |
| Frattini | C2 | C7×D127⋊C7 |
| Fitting, socle | C2×C7×C127 | C2×C7 |
| prime radical | C2×C7×C127⋊C7 | C2 |
| cosocle | C2×C127 | C2×C72 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C2×C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3556 |
322 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24892, 15);