Finite Group DatabasebetaFinite Group Databasebeta| order | 33708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #30682883⋊C2 |
| unambiguous semidirect product | ((C53⋊D53)⋊C3)⋊C2 |
| Fitting, socle, Sylow | C532 ⋊ C2×D3 |
| derived, Hall | C532⋊C3 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C532⋊C3 | C22 |
| Fitting, socle | C532 | C2×D3 |
| LCS | G ▷ C532⋊C3 | |
| UCS | C1 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 159 |
Polycyclic presentation:
2^2,3,53^2|c^a=c^2,d^a=d^52e^49,c^b=c^2,d^b=de^4,e^b=e^52,d^c=d^21e^48,e^c=d^29e^31318 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33708, 25);