Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D33⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×D33⋊C3 |
| unambiguous semidirect product | (C2×D33)⋊C3 |
| Fitting, socle | C2×C33 ⋊ C2×A4 |
| derived | #1113 ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D33⋊C3 |
| commutator, cosocle, hypocenter | #1113 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C33 | C2×A4 |
| LCS | G ▷ #1113 | |
| UCS | C1 ◁ C2 | |
268 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 18 |
34 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10620184⋊C2, C22×D33⋊C3 |
| maximal normal subgroup of | C2×#10620184⋊C2, C22×D33⋊C3 |
| maximal quotient of | C22×D33⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3494);