Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25×C4 |
| direct product | C7×#21232 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
1470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7)(9,11)(12,13,14,15)(16,17)(18,28)(19,33)(20,25)(21,26)(22,27)(23,31)(24,35)(29,37)(30,39)(32,38)(34,41)(36,40)(42,43)(44,46)(45,47);(8,9,10,11)(13,15)(16,18,20,31,22,32,21,30)(17,23,26,28,27,39,25,38)(19,29,34,44,36,45,35,43)(24,37,40,42,41,47,33,46);(16,19,20,34,22,36,21,35)(17,24,26,40,27,41,25,33)(18,29,31,44,32,45,30,43)(23,37,28,42,39,47,38,46);(16,20,22,21)(17,25,27,26)(18,30,32,31)(19,34,36,35)(23,28,39,38)(24,33,41,40)(29,43,45,44)(37,42,47,46)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14220);