Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C32 · Schur multiplier (H2) = C23 |
| direct product | C7×D4×C32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C7×C32 | C22 |
| commutator | C2 | C22×C7×C32 |
| Frattini, cosocle | C2×C16 | C23×C7 |
| socle | C22×C7 | C22×C16 |
| prime radical | C2×C7×D4 | C16 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7×C32 ◁ G | |
214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,10,11);(9,11);(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43)1120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6632);