Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C4 |
| direct product | C2×#13834⋊C3 |
| Fitting, Sylow | C2×#13834 ⋊ C3 |
| derived | #13834 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C22⋊(C42⋊C3) |
| commutator, cosocle, hypocenter | #13834 | C2×C3 |
| Frattini | C24 | C2×C22⋊A4 |
| Fitting | C2×#13834 | C3 |
| socle | C25 | C22⋊A4 |
| LCS | G ▷ #13834 | |
| UCS | C1 ◁ C23 | |
1617 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 1617 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #72267018, C2×#72210818, #72267047, … |
| maximal normal subgroup of | C2×#72210818 |
Past the SmallGroups library coverage — no SmallGroups id.