Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24390 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#24519 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#449 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
986 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)(14,18)(15,17)(16,19)(20,21,26,29,25,30,24,31)(22,32,33,35,23,27,34,28);(8,9)(10,11)(12,14,15,19)(13,16,17,18)(20,22,25,23)(21,27,30,32)(24,34,26,33)(28,31,35,29);(9,11)(20,23,25,22)(21,28,30,35)(24,34,26,33)(27,31,32,29);(13,17)(16,18)(20,24,25,26)(21,29,30,31)(22,33,23,34)(27,35,32,28)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17507);