Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#91877 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C2×S5 |
| commutator, cosocle, hypocenter | SL(2,𝔽5) | C22×C3 |
| Frattini | C2 | C2×C3×S5 |
| Fitting, hypercenter | C22×C3 | S5 |
| LCS | G ▷ SL(2,𝔽5) | |
| UCS | C1 ◁ C2×C3 ◁ C22×C3 | |
142 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 144 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | #72277272 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4627);