Finite Group DatabasebetaFinite Group Databasebeta| order | 33855 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20270133⋊C5 |
| Fitting, socle, derived, Hall | C37×C61 ⋊ C3×C5 |
| Hall | C37×C61⋊C5 ⋊ C3 |
| Hall | #20270133 ⋊ C5 |
| Hall | C61⋊C5 ⋊ C37⋊C3 |
| Sylow | C61 ⋊ C5×C37⋊C3 |
| Sylow | C37 ⋊ (C61⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C61 | C3×C5 |
| LCS | G ▷ C37×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2257 |
Polycyclic presentation:
3,5,37,61|c^a=c^26,d^a=d^47,d^b=d^9223 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33855, 9);