Finite Group DatabasebetaFinite Group Databasebeta| order | 25972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C43 · Schur multiplier (H2) = C2 |
| direct product | C2×C43×D151 |
| unambiguous semidirect product | C151⋊(C22×C43) |
| unambiguous semidirect product | (C2×C151)⋊(C2×C43) |
| Fitting, socle | C2×C43×C151 ⋊ C2 |
| derived, Sylow | C151 ⋊ C22×C43 |
| Hall | C43×C151 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C43 | D151 |
| commutator, cosocle, hypocenter | C151 | C22×C43 |
| Frattini | C1 | G |
| Fitting, socle | C2×C43×C151 | C2 |
| LCS | G ▷ C151 | |
| UCS | C1 ◁ C2×C43 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12986 |
6622 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25972, 7);