Finite Group DatabasebetaFinite Group Databasebeta| order | 34100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C31⋊#1042 |
| unambiguous semidirect product | C31⋊(C11×#1042) |
| Fitting, socle, Hall | C52×C11×C31 ⋊ C4 |
| derived, Hall | C52×C31 ⋊ C4×C11 |
| Hall | C11×C31 ⋊ #1042 |
| Hall | C52×C11 ⋊ Dic31 |
| Sylow | C31 ⋊ C11×#1042 |
| Sylow | C52 ⋊ C11×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C31⋊#1042 |
| commutator, hypocenter | C52×C31 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C11×C31 | C4 |
| prime radical | C5×D5×C11×C31 | C2 |
| cosocle | C5×D5×C31 | C2×C11 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 ◁ C11 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6820 |
3443 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34100, 278);