Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #88941 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#88941 |
| Sylow | C34 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #157⋊D3 |
| commutator, cosocle | C3×C3⋊Dic3 | C22×C3 |
| Frattini | C2 | C3×#157⋊D3 |
| Fitting, socle | C2×C34 | D4 |
| hypocenter | C33 | C3×D8 |
| LCS | G ▷ C3×C3⋊Dic3 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2×C3 | |
290 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | #72220232, C3×#11724350, #72220276 |
| maximal normal subgroup of | #72220232, C3×#11724350, #72220276 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3146);