Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #6881 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C9 |
| direct product | C2×C4×#6881 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4 | #732 |
| commutator | C3×C9 | C2×C32×C4 |
| Frattini, cosocle | C2×C3×C9 | C22×C32 |
| socle | C22×C3 | C2×#732 |
| prime radical | C22×#6881 | C2 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4 ◁ C2×C32×C4 ◁ C2×C3×C4×C9 ◁ G | |
168 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2)(7,8,11)(9,16,20)(10,15,21)(12,22,18)(13,25,17)(14,27,19)(23,32,30)(24,31,29)(26,33,28);(3,4,5,6)(8,12,13,15,24,26,14,23,16)(9,17,28)(11,20,31,27,33,22,21,25,32)(18,30,29)152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 612);