Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D3×D92 |
| Fitting | C2×C3×C92 ⋊ C23 |
| derived, Sylow | C3×C92 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D92 |
| commutator, cosocle, hypocenter | C3×C92 | C24 |
| Frattini | C32 | C2×D33 |
| Fitting | C2×C3×C92 | C23 |
| socle | C2×C33 | C2×D32 |
| LCS | G ▷ C3×C92 | |
| UCS | C1 ◁ C2 | |
1692 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1692 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#13047160, D32×D92, C2×D3×#92265⋊C2 |
| maximal normal subgroup of | D3×#13047160, C2×D3×#92265⋊C2 |
| maximal quotient of | D3×#13047160, D32×D92 |
Past the SmallGroups library coverage — no SmallGroups id.