Finite Group DatabasebetaFinite Group Databasebeta| order | 24745 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×C101⋊C5 |
| unambiguous semidirect product | C101⋊(C5×C72) |
| unambiguous semidirect product | (C7×C101)⋊(C5×C7) |
| unambiguous semidirect product | (C72×C101)⋊C5 |
| Fitting, socle, Hall | C72×C101 ⋊ C5 |
| derived, Sylow | C101 ⋊ C5×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | C101⋊C5 |
| commutator, cosocle, hypocenter | C101 | C5×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C101 | C5 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4949 |
1225 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24745, 4);