Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C211 |
| direct product | C22×#11710929 |
| Fitting, Sylow | C24×#585 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | C22⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C22×H(5,𝔽2) | C23×C3 |
| Frattini | C2 | C23×C22⋊(C22⋊A4) |
| Fitting | C24×#585 | C3 |
| socle | C25 | C2×C22⋊A4 |
| LCS | G ▷ C22×H(5,𝔽2) | |
| UCS | C1 ◁ C22×C4 | |
Only the 742 normal subgroups are shown; non-normal subgroups are omitted.
Only the group's 742 normal subgroups are shown; non-normal subgroups are omitted.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
224 conjugacy classes — view the full character table.
| maximal subgroup of | #72267348, #72267358, #72267522 |
| maximal normal subgroup of | #72267358 |
Past the SmallGroups library coverage — no SmallGroups id.