Finite Group DatabasebetaFinite Group Databasebeta| order | 4608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C3×#11709313 |
| Fitting | C2×C3×#15947 ⋊ C3 |
| derived | #15947 ⋊ C2×C32 |
| Sylow | C2×#15947 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | #5464 |
| commutator, cosocle, hypocenter | #15947 | C2×C32 |
| Frattini | C24 | C2×C3×C22⋊A4 |
| Fitting | C2×C3×#15947 | C3 |
| socle | C25×C3 | C22⋊A4 |
| LCS | G ▷ #15947 | |
| UCS | C1 ◁ C23×C3 | |
19628 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 19628 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#72209884 |
| maximal normal subgroup of | C2×C3×#72209884 |
Past the SmallGroups library coverage — no SmallGroups id.