Finite Group DatabasebetaFinite Group Databasebeta| order | 4356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10624391⋊D3 |
| Fitting, socle | C3×C112 ⋊ C2×D3 |
| derived, Hall | C3×C112⋊C3 ⋊ C22 |
| Sylow | C112 ⋊ D32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C112⋊C3 | C22 |
| Fitting, socle | C3×C112 | C2×D3 |
| LCS | G ▷ C3×C112⋊C3 | |
| UCS | C1 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 99 |
Polycyclic presentation:
2^2,3^2,11^2|d^a=d^2,e^a=e^10,f^a=f^10,c^b=c^2,e^b=e^3f^10,f^b=e^8f^8,e^c=e^2f^10,f^c=e^7f^869 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4356, 80);