Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2×C5 |
| direct product | D11×C31×C5⋊D5 |
| unambiguous semidirect product | (C5×D11)⋊(D5×C31) |
| Fitting, socle, Hall | C52×C11×C31 ⋊ C22 |
| derived, Hall | C52×C11 ⋊ C22×C31 |
| Hall | C52×C31 ⋊ C2×D11 |
| Hall | C11×C31 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×D11×C31 |
| Sylow | C11 ⋊ C2×C31×C5⋊D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D11×C5⋊D5 |
| commutator, cosocle, hypocenter | C52×C11 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C52×C11×C31 | C22 |
| LCS | G ▷ C52×C11 | |
| UCS | C1 ◁ C31 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8525 |
3038 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 293);