Finite Group DatabasebetaFinite Group Databasebeta| order | 25172 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C7⋊#1181 |
| unambiguous semidirect product | C7⋊(C31×#1181) |
| Fitting, socle, Hall | C7×C29×C31 ⋊ C4 |
| derived, Hall | C7×C29 ⋊ C4×C31 |
| Hall | C29×C31 ⋊ Dic7 |
| Hall | C7×C31 ⋊ #1181 |
| Sylow | C29 ⋊ Dic7×C31 |
| Sylow | C7 ⋊ C31×#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C7⋊#1181 |
| commutator, hypocenter | C7×C29 | C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C7×C29×C31 | C4 |
| prime radical | C7×C31×D29 | C2 |
| cosocle | C7×D29 | C2×C31 |
| LCS | G ▷ C7×C29 | |
| UCS | C1 ◁ C31 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6293 |
1829 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25172, 25);