Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #15257 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C22×C42 |
| direct product | C7×#15944 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1234 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(9,11)(14,18)(17,19)(20,21)(22,24)(23,26)(25,27)(28,29,32,31)(30,34,35,33);(13,16)(17,19)(21,22)(23,27)(28,30,32,35)(29,33,31,34);(12,13,15,16)(14,17,18,19)(20,22,24,21)(23,26,27,25)(28,31,32,29)(30,33,35,34);(8,9)(10,11)(12,14,15,18)(13,17,16,19)(20,23)(21,25)(22,26)(24,27)(28,30)(29,34)(31,33)(32,35)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 8932);