Finite Group DatabasebetaFinite Group Databasebeta| order | 3888 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D3×(((C3⋊D3)⋊C3)⋊C2)⋊D3 |
| Fitting, Sylow | C32×H(3,𝔽3) ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | C32×#272 | C23 |
| Frattini | C3 | D3×D32⋊D3 |
| Fitting, hypocenter | C32×H(3,𝔽3) | C2×D4 |
| socle | C33 | C2×GO+(4,𝔽2) |
| LCS | G ▷ C32×#272 ▷ C32×H(3,𝔽3) | |
| UCS | C1 | |
971 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 971 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | #72259881 |
Past the SmallGroups library coverage — no SmallGroups id.