Finite Group DatabasebetaFinite Group Databasebeta| order | 3310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D331⋊C5 |
| unambiguous semidirect product | (C331⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C331 ⋊ C2×C5 |
| Hall | C331⋊C5 ⋊ C2 |
| Hall | D331 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C331 | C2×C5 |
| LCS | G ▷ C331 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 331 |
| transitive degree | μt(G) = 331 |
Polycyclic presentation:
2,5,331|c^a=c^330,c^b=c^6443 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D331⋊C5, C5⋊(D331⋊C5), C7×D331⋊C5, … |
| maximal normal subgroup of | C5×D331⋊C5, C7×D331⋊C5, C11×D331⋊C5, … |
| maximal quotient of | D331⋊C25, C5×D331⋊C5, C5⋊(D331⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3310, 1);