Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#26050 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C4×C7×C4⋊C4 ◁ G | |
758 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)(9,10)(12,13,15,17)(14,18,19,16)(20,21,23,26)(22,28,30,25)(24,27,32,34)(29,33,31,35);(8,9,11,10)(20,22,23,30)(21,25,26,28)(24,29,32,31)(27,35,34,33);(12,14,15,19)(13,16,17,18)(21,26)(22,29)(24,32)(25,33)(28,35)(30,31);(8,10,11,9)(21,26)(25,28)(27,34)(33,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 19038);