Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C5×D11×D31⋊C5 |
| unambiguous semidirect product | D31⋊(C52×D11) |
| Fitting, socle | C5×C11×C31 ⋊ C22×C5 |
| derived, Hall | C11×C31 ⋊ C22×C52 |
| Hall | C5×C11×ΓL(1,𝔽32) ⋊ C22 |
| Hall | D11×D31 ⋊ C52 |
| Hall | C5×ΓL(1,𝔽32) ⋊ C2×D11 |
| Sylow | C31 ⋊ C2×C52×D11 |
| Sylow | C11 ⋊ C2×C5×D31⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D11×D31⋊C5 |
| commutator, cosocle, hypocenter | C11×C31 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C31 | C22×C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C5 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1705 |
455 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 157);