Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C35 · Schur multiplier (H2) = C2×C310 |
| direct product | C35×D4 |
| unambiguous semidirect product | C4⋊(C2×C35) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C35 | C22 |
| commutator, Frattini, cosocle | C2 | C22×C35 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C35 ◁ G | |
21312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 972 |
A minimal faithful permutation representation — 5 generators on 19 points:
(1,2,3)(16,17,18,19);(4,5,6)(17,19);(7,8,9);(10,11,12);(13,14,15)1215 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3872);