Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3186 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#21939 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C25×C7 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C24×C4×C7 ◁ G | |
1122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,10,11)(12,13)(14,18)(15,17)(16,19)(20,21)(22,26)(23,30)(24,33)(25,28)(27,31)(29,34)(32,35);(12,14)(13,16)(15,19)(17,18)(20,22,25,24)(21,26,28,33)(23,29,32,31)(27,30,34,35);(14,19)(16,18)(20,23,24,31,25,32,22,29)(21,27,26,30,28,34,33,35);(13,17)(16,18)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14927);