Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9125 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C24×C7 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G | |
530 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(13,16,17,18)(20,21,24,27,25,28,23,33)(22,29,32,34,30,35,31,26);(12,13,14,18,15,17,19,16)(20,22,25,30)(21,26)(23,31,24,32)(27,29)(28,34)(33,35);(9,11)(22,30)(26,34)(29,35)(31,32)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2113);