Finite Group DatabasebetaFinite Group Databasebeta| order | 33708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D159⋊D53 |
| Fitting, socle, derived, Hall | C3×C532 ⋊ C22 |
| Sylow | C532 ⋊ C2×D3 |
| Sylow | C3 ⋊ D532 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C532 | C22 |
| LCS | G ▷ C3×C532 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 318 |
Polycyclic presentation:
2^2,3,53^2|c^a=c^2,d^a=d^52,d^b=d^52,e^b=e^522190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33708, 37);