Finite Group DatabasebetaFinite Group Databasebeta| order | 34572 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C43×C67 ⋊ C3×C4 |
| Hall | C43×Dic67 ⋊ C3 |
| Hall | #22575687 ⋊ C4 |
| Hall | Dic67 ⋊ C43⋊C3 |
| Sylow | C67 ⋊ C4×C43⋊C3 |
| Sylow | C43 ⋊ (C67⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #31772251 |
| commutator, hypocenter | C43×C67 | C3×C4 |
| Fitting, socle, cosocle | C2×C43×C67 | C2×C3 |
| prime radical | C2×#22575687 | C2 |
| LCS | G ▷ C43×C67 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11524 |
Polycyclic presentation:
2,3,43,67,2|a^2=e,d^a=d^66,c^b=c^36,d^b=d^291014 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34572, 16);