Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×S5 |
| commutator, socle, prime radical, cosocle | C2×C3×A5 | C22 |
| Fitting | C2×C3 | C2×S5 |
| hypocenter | C3×A5 | Q8 |
| LCS | G ▷ C2×C3×A5 ▷ C3×A5 | |
| UCS | C1 ◁ C2 | |
157 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 157 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,7,4,2)(3,5,8,6)(11,13,12)(14,15);(1,8,4,3)(2,6,7,5)(9,13,11,10)(14,16)33 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4599);