Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C211 |
| direct product | C23×C22⋊#997 |
| Fitting, Sylow | C25×H(5,𝔽2) ⋊ C3 |
| derived | C22×H(5,𝔽2) ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C22×H(5,𝔽2) | C23×C3 |
| Frattini | C2 | C23×C22⋊(C22⋊A4) |
| Fitting | C25×H(5,𝔽2) | C3 |
| socle | C26 | C22⋊A4 |
| LCS | G ▷ C22×H(5,𝔽2) | |
| UCS | C1 ◁ C24 | |
2957356 conjugacy classes of subgroups; only the 822 normal subgroups are shown.
This group has 2957356 conjugacy classes of subgroups — too many to draw. Only its 822 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
224 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.