Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C27 |
| direct product | C2×#11710650 |
| Fitting, Sylow | C23×H(3,𝔽4) ⋊ C3 |
| derived | C26 ⋊ C23×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11710650 |
| commutator, cosocle, hypocenter | C26 | C23×C3 |
| Frattini | C22 | C23×C22⋊A4 |
| Fitting | C23×H(3,𝔽4) | C3 |
| socle | C25 | C22×A4 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C2 | |
17350 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 17350 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72234656, C2×A4×#5450 |
| maximal normal subgroup of | C2×#72234656, C2×A4×#5450 |
Past the SmallGroups library coverage — no SmallGroups id.