Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33×C4 · Schur multiplier (H2) = C2×C34 |
| direct product | C33×C4×C3⋊D3 |
| Fitting | C35×C4 ⋊ C2 |
| derived | C32 ⋊ C2×C33×C4 |
| Sylow | C35 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33×C4 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C33×C4 |
| Frattini | C2 | C2×C33×C3⋊D3 |
| Fitting | C35×C4 | C2 |
| socle | C2×C35 | C22 |
| prime radical | C2×C33×C3⋊D3 | C2 |
| cosocle | C2×C32 | C22×C33 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C33×C4 | |
5088 conjugacy classes of subgroups; only the 644 normal subgroups are shown.
This group has 5088 conjugacy classes of subgroups — too many to draw. Only its 644 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3852);