Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×Dic341 |
| derived, Hall | C11×C31 ⋊ C4×C25 |
| Hall | C11×C25×C31 ⋊ C4 |
| Hall | C25×C31 ⋊ Dic11 |
| Hall | C11×C25 ⋊ Dic31 |
| Sylow | C31 ⋊ C25×Dic11 |
| Sylow | C11 ⋊ C25×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D341 |
| commutator, hypocenter | C11×C31 | C4×C25 |
| Frattini | C2×C5 | C5×D341 |
| Fitting | C2×C11×C25×C31 | C2 |
| socle, prime radical, cosocle | C2×C5×C11×C31 | C2×C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C2×C25 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34100 |
8600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 10);