Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C213 |
| direct product | C23×#87545 |
| Fitting, Sylow | C25×2−1+4 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×C22⋊A4 |
| commutator, cosocle, hypocenter | C22×Q8 | C25×C3 |
| Frattini | C2 | C25×C22⋊A4 |
| Fitting | C25×2−1+4 | C3 |
| socle | C26 | C22×A4 |
| hypercenter | C23×D4 | C22⋊A4 |
| LCS | G ▷ C22×Q8 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
2787303 conjugacy classes of subgroups; only the 3094 normal subgroups are shown.
This group has 2787303 conjugacy classes of subgroups — too many to draw. Only its 3094 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72267937, #72267959 |
| maximal normal subgroup of | #72267959 |
Past the SmallGroups library coverage — no SmallGroups id.