Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #67156 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#67157 |
| Hall | C32×C5 ⋊ C22×D4 |
| Sylow | C32 ⋊ C22×D20 |
| Sylow | C5 ⋊ C22×#625 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | (C3⋊D3)⋊D5 |
| commutator, cosocle | C2×C32×C5 | C24 |
| Frattini | C2 | C22×(C3⋊D3)⋊D5 |
| Fitting, socle | C23×C32×C5 | C22 |
| hypocenter | C32×C5 | C22×D4 |
| LCS | G ▷ C2×C32×C5 ▷ C32×C5 | |
| UCS | C1 ◁ C23 | |
998 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 223 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5746);