Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #10619745 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×#10619745 |
| Fitting | C22×C3×H(3,𝔽3) ⋊ D3 |
| derived | C32×A4 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10619745 |
| commutator, cosocle, hypocenter | C32×A4 | C2×C32 |
| Frattini | C32 | C32×S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C32×A4 | |
| UCS | C1 ◁ C3 | |
324 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
69 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2374);