Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C92 · Schur multiplier (H2) = C2×C32×C9 |
| direct product | C3×D4×C92 |
| unambiguous semidirect product | C4⋊(C2×C3×C92) |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C92 | C22 |
| commutator | C2 | C22×C3×C92 |
| Frattini, cosocle | C2×C32 | C22×C33 |
| socle | C2×C33 | C22×C32 |
| prime radical | C33×D4 | C32 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C92 ◁ G | |
1008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 972 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,3)(22,23,24,25);(4,5,6,7,8,9,10,11,12)(23,25);(13,14,15,16,17,18,19,20,21)1215 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2193);