Finite Group DatabasebetaFinite Group Databasebeta| order | 34465 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C113 · Schur multiplier (H2) = C1 |
| direct product | C113×C61⋊C5 |
| unambiguous semidirect product | C61⋊(C5×C113) |
| unambiguous semidirect product | (C61×C113)⋊C5 |
| Fitting, socle, Hall | C61×C113 ⋊ C5 |
| derived, Sylow | C61 ⋊ C5×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | C61⋊C5 |
| commutator, cosocle, hypocenter | C61 | C5×C113 |
| Frattini | C1 | G |
| Fitting, socle | C61×C113 | C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C113 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6893 |
1921 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34465, 1);