Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D32⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D32⋊(C3⋊D3) |
| unambiguous semidirect product | D32⋊(C3×C3⋊D3) |
| Fitting, socle, Sylow | C35 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D32⋊(C3⋊D3) |
| commutator, cosocle | C32×C3⋊D3 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C35 | D4 |
| hypocenter | C34 | C3×D4 |
| LCS | G ▷ C32×C3⋊D3 ▷ C34 | |
| UCS | C1 ◁ C3 | |
1124 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | #72228576 |
| maximal normal subgroup of | #72228576 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3910);