Finite Group DatabasebetaFinite Group Databasebeta| order | 34572 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #31772250⋊C2 |
| unambiguous semidirect product | #31772254⋊C2 |
| unambiguous semidirect product | #31772258⋊C2 |
| Fitting, socle, derived, Hall | C43×C67 ⋊ C22×C3 |
| Hall | D43×D67 ⋊ C3 |
| Hall | #22575686 ⋊ C22 |
| Sylow | C67 ⋊ C2×D43⋊C3 |
| Sylow | C43 ⋊ C2×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C67 | C22×C3 |
| LCS | G ▷ C43×C67 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2881 |
Polycyclic presentation:
2^2,3,43,67|e^a=e^66,d^b=d^42,d^c=d^36,e^c=e^37279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34572, 27);