Finite Group DatabasebetaFinite Group Databasebeta| order | 3110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C311⋊C5 |
| unambiguous semidirect product | (C2×C311)⋊C5 |
| Fitting, socle, Hall | C2×C311 ⋊ C5 |
| derived, Sylow | C311 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C311⋊C5 |
| commutator, cosocle, hypocenter | C311 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C311 | C5 |
| LCS | G ▷ C311 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 313 |
| transitive degree | μt(G) = 622 |
134 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C311⋊C5, C2×C5×C311⋊C5, C2×C7×C311⋊C5, … |
| maximal normal subgroup of | C2×C5×C311⋊C5, C2×C7×C311⋊C5, C2×C11×C311⋊C5 |
| maximal quotient of | C2×C311⋊C25, D5×C311⋊C5, C2×C5×C311⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3110, 2);