Finite Group DatabasebetaFinite Group Databasebeta| order | 34692 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×#10596868 |
| derived, Hall | #3862 ⋊ C4×C59 |
| Hall | C59×#3862 ⋊ C4 |
| Hall | C72×C59 ⋊ Dic3 |
| Sylow | C72 ⋊ Dic3×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C59 | #64418 |
| commutator, hypocenter | #3862 | C4×C59 |
| Frattini | C2 | C59×#64418 |
| Fitting, socle | C2×C72×C59 | D3 |
| prime radical | C2×C59×#3862 | C2 |
| cosocle | C2×#3862 | C2×C59 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C2×C59 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1652 |
2360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34692, 53);