Finite Group DatabasebetaFinite Group Databasebeta| order | 32395 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#13133724 |
| Fitting, socle, Hall | C11×C19×C31 ⋊ C5 |
| derived, Hall | C11×C31 ⋊ C5×C19 |
| Hall | C19×C31 ⋊ C11⋊C5 |
| Hall | C11×C19 ⋊ ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C19×C11⋊C5 |
| Sylow | C11 ⋊ C19×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #13133724 |
| commutator, cosocle, hypocenter | C11×C31 | C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C11×C19×C31 | C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6479 |
1387 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32395, 7);