Finite Group DatabasebetaFinite Group Databasebeta| order | 19425 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×#11715912 |
| Fitting, socle, Hall | C52×C7×C37 ⋊ C3 |
| derived, Hall | C7×C37 ⋊ C3×C52 |
| Hall | C52×C37 ⋊ ΓL(1,𝔽8) |
| Hall | C52×C7 ⋊ C37⋊C3 |
| Sylow | C37 ⋊ C52×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C52×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | #11715912 |
| commutator, cosocle, hypocenter | C7×C37 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C37 | C3 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6475 |
2225 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19425, 13);