Finite Group DatabasebetaFinite Group Databasebeta| order | 3110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D311⋊C5 |
| unambiguous semidirect product | (C311⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C311 ⋊ C2×C5 |
| Hall | C311⋊C5 ⋊ C2 |
| Hall | D311 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C311 | C2×C5 |
| LCS | G ▷ C311 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 311 |
| transitive degree | μt(G) = 311 |
Polycyclic presentation:
2,5,311|c^a=c^310,c^b=c^3641 conjugacy classes — view the full character table.
| maximal subgroup of | C5×D311⋊C5, C5⋊(D311⋊C5), C7×D311⋊C5, … |
| maximal normal subgroup of | C5×D311⋊C5, C7×D311⋊C5, C11×D311⋊C5 |
| maximal quotient of | D311⋊C25, C5×D311⋊C5, C5⋊(D311⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3110, 1);