Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#11926 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#102 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C4×C8 | C23×C7 |
| prime radical | C22×C7×D8 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ C2×C4×C7×C8 ◁ G | |
418 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,10,13,11,12,14,15)(16,17)(18,28,31,45)(19,24)(20,34)(21,26)(22,27)(23,30,39,46)(25,36)(29,44,32,41)(33,43)(35,40,47,38)(37,42);(9,12)(10,14)(16,18)(17,23)(19,32)(20,35)(21,29)(22,31)(24,40)(25,41)(26,38)(27,39)(28,42)(30,33)(34,45)(36,46)(37,47)(43,44);(16,19,22,21)(17,24,27,26)(18,29,31,32)(20,33,37,36)(23,38,39,40)(25,34,43,42)(28,44,45,41)(30,35,46,47)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4914);