Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C3×#88813 |
| derived | C33 ⋊ C3×C42 |
| Sylow | C34 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #1113 |
| commutator, hypocenter | C33 | C3×C42 |
| Frattini | C22 | C3×#1113 |
| Fitting, socle, prime radical | C22×C34 | C22 |
| cosocle | C22×C33 | C22×C3 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C22×C3 | |
650 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #72220315, C3×#11723728, #72220328 |
| maximal normal subgroup of | #72220315, C3×#11723728, #72220328 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2756);