Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8×C9 · Schur multiplier (H2) = C34 |
| direct product | C3×C8×C32⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center | C33×C8 | C32 |
| commutator | C3 | C32×C8×C9 |
| Frattini, cosocle | C32×C4 | C2×C33 |
| socle | C2×C33 | C32×C4 |
| prime radical | C2×C34 | C3×C4 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C8 ◁ G | |
576 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 648 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3)(22,23,24,25,26,27,28,29);(4,5,7)(6,9,11)(8,12,10)(13,14,16,15,17,19,18,20,21);(5,8,9)(7,11,12)792 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 773);