Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#22057 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
968 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)(8,9,11,10)(12,13)(14,18)(15,17)(16,19)(20,21,25,29)(22,26,31,35)(23,28,24,33)(27,32,34,30);(8,10,11,9)(12,14)(13,16)(15,19)(17,18)(20,22)(21,26)(23,32)(24,30)(25,31)(27,33)(28,34)(29,35);(14,19)(16,18)(20,22)(21,27)(23,30)(24,32)(25,31)(26,33)(28,35)(29,34);(13,17)(16,18)(20,23,25,24)(21,28,29,33)(22,30,31,32)(26,27,35,34)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15045);