Finite Group DatabasebetaFinite Group Databasebeta| order | 25452 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C101 · Schur multiplier (H2) = C2 |
| direct product | D3×D21×C101 |
| unambiguous semidirect product | (C3×D3)⋊(D7×C101) |
| unambiguous semidirect product | (D3×C7)⋊(D3×C101) |
| Fitting, socle, Hall | C32×C7×C101 ⋊ C22 |
| derived, Hall | C32×C7 ⋊ C22×C101 |
| Hall | C32×C101 ⋊ C2×D7 |
| Hall | C7×C101 ⋊ D32 |
| Sylow | C32 ⋊ C2×D7×C101 |
| Sylow | C7 ⋊ D32×C101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C101 | D3×D21 |
| commutator, cosocle, hypocenter | C32×C7 | C22×C101 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C101 | C22 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C101 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4242 |
3636 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25452, 101);