Finite Group DatabasebetaFinite Group Databasebeta| order | 3310 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D331 |
| Fitting, socle, Hall | C5×C331 ⋊ C2 |
| derived, Sylow | C331 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D331 |
| commutator, cosocle, hypocenter | C331 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C331 | C2 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 336 |
| transitive degree | μt(G) = 1655 |
835 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D331⋊C25, C25×D331, C5×D331⋊C5, … |
| maximal normal subgroup of | D331⋊C25, C25×D331, C5×D331⋊C5, … |
| maximal quotient of | C25×D331, C5×D1655, C52×D331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3310, 4);