Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#23797 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C23×C7 | C22×D4 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ C43×C7 ◁ G | |
1018 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)(14,17,18,19)(20,21,23,27,25,29,24,28)(22,30,31,35,33,34,32,26);(8,9)(10,11)(13,16)(17,19)(20,22,25,33)(21,26,29,35)(23,32,24,31)(27,34,28,30);(9,11)(21,27)(23,24)(26,34)(28,29)(30,35)(31,32);(12,14,15,18)(13,17,16,19)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16785);