Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#17072⋊C3 |
| Fitting, Sylow | C2×#17072 ⋊ C3 |
| derived | #17072 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #5464 |
| commutator, cosocle, hypocenter | #17072 | C2×C3 |
| Frattini | C24 | C2×C22⋊A4 |
| Fitting | C2×#17072 | C3 |
| socle | C25 | C22⋊A4 |
| LCS | G ▷ #17072 | |
| UCS | C1 ◁ C23 | |
1812 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | #72267047 |
Past the SmallGroups library coverage — no SmallGroups id.