Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D3×#4178⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| Fitting, derived, Sylow | C3×#732 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×#732 | C23 |
| Frattini | C32 | D33 |
| socle | C32 | C2×((C3⋊D3)⋊C3)⋊C2 |
| LCS | G ▷ C3×#732 | |
| UCS | C1 | |
432 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 54 |
51 conjugacy classes — view the full character table.
| maximal subgroup of | #72244020, D3×#92280⋊C2, #72244025, … |
| maximal normal subgroup of | D3×(#4178⋊C2)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2346);