Finite Group DatabasebetaFinite Group Databasebeta| order | 3310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C331⋊C5 |
| unambiguous semidirect product | (C2×C331)⋊C5 |
| Fitting, socle, Hall | C2×C331 ⋊ C5 |
| derived, Sylow | C331 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C331⋊C5 |
| commutator, cosocle, hypocenter | C331 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C331 | C5 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 333 |
| transitive degree | μt(G) = 662 |
142 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C331⋊C5, C2×C5×C331⋊C5, C2×C7×C331⋊C5, … |
| maximal normal subgroup of | C2×C5×C331⋊C5, C2×C7×C331⋊C5, C2×C11×C331⋊C5, … |
| maximal quotient of | C2×C331⋊C25, D5×C331⋊C5, C2×C5×C331⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3310, 2);