Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1468 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C22×C4 |
| direct product | C7×#7914 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G | |
666 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)(12,13,15,19,16,17,14,18)(20,21)(22,28,30,25)(23,26)(24,27)(29,34,35,32)(31,33);(8,9,10,11)(13,17)(14,15)(20,22)(21,25)(23,29)(24,30)(26,32)(27,28)(31,35)(33,34);(12,14,16,15)(13,18,17,19)(20,23,24,31)(21,26,27,33)(22,29,30,35)(25,32,28,34)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 902);