Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C3×D4×#1113 |
| Fitting | C34×D4 ⋊ C22 |
| Sylow | C34 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C22×#1113 |
| commutator, cosocle | C2×C33 | C24×C3 |
| Frattini | C2 | C22×C3×#1113 |
| Fitting | C34×D4 | C22 |
| socle | C2×C34 | C24 |
| hypercenter | C3×D4 | #1113 |
| hypocenter | C33 | C22×C3×D4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2×C3 ◁ C3×D4 | |
2970 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 2970 conjugacy classes of subgroups — too many to draw. Only its 318 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | D4×(((C3⋊D3)⋊C9)⋊C2)⋊C3, D4×#11757730 |
| maximal quotient of | D4×(#4207⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.