Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#21132 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C7×#376 ◁ G | |
814 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1792 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13)(14,17)(15,16)(18,19)(20,21,26,31)(22,27,23,33)(24,30,25,29)(28,32,35,34);(8,10,11,9)(13,16)(17,19)(20,22,26,23)(21,27,31,33)(24,34,25,32)(28,29,35,30);(20,23,26,22)(21,28,31,35)(24,34,25,32)(27,29,33,30);(12,14,15,18)(13,17,16,19)(20,24,26,25)(21,29,31,30)(22,32,23,34)(27,28,33,35)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14120);