Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #10620197 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#10620197 |
| Fitting, socle, Sylow | C35 ⋊ C2×C4 |
| derived | C34 ⋊ C2×C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10620197 |
| commutator, hypocenter | C34 | C2×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C35 | C2×C4 |
| prime radical | C3×C3⋊D32 | C2 |
| cosocle | C32×C3⋊D3 | C22×C3 |
| LCS | G ▷ C34 | |
| UCS | C1 ◁ C3 | |
812 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(D32⋊D3)⋊D3, C3×D32⋊#157, #72228623, … |
| maximal normal subgroup of | C3×(D32⋊D3)⋊D3, C3×D32⋊#157, #72228623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3897);