Finite Group DatabasebetaFinite Group Databasebeta| order | 25172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C29×C31 ⋊ C22×C7 |
| Hall | C31×C29⋊C7 ⋊ C22 |
| Hall | D29×D31 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×D29⋊C7 |
| Sylow | C29 ⋊ C2×C7×D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C31 | C22×C7 |
| LCS | G ▷ C29×C31 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 899 |
272 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25172, 16);