Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#26918 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C4×C7×C4⋊C4 ◁ G | |
830 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(12,13,15,16)(14,18,19,17)(20,21,25,29,26,30,24,28)(22,31,33,27,23,34,32,35);(8,9)(10,11)(13,16)(17,18)(20,22,26,23)(21,27,30,35)(24,33,25,32)(28,34,29,31);(9,11)(20,23,26,22)(21,27,30,35)(24,32,25,33)(28,34,29,31);(12,14,15,19)(13,17,16,18)(21,28)(24,25)(27,34)(29,30)(31,35)(32,33)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 19906);