Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9331 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9339 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C7×#121 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
416 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,13,12,10,15,14)(16,17)(18,27)(19,31,34,41)(20,35)(21,25)(22,26)(23,29)(24,33,40,32)(28,43,45,37)(30,38)(36,39)(42,44,47,46);(8,10)(9,12)(11,13)(14,15)(16,18,20,29,22,30,21,36)(17,23,25,27,26,39,35,38)(19,28,33,46,34,45,32,44)(24,37,41,42,40,43,31,47);(8,9)(10,12)(11,13)(14,15)(16,19)(17,24)(18,28)(20,33)(21,32)(22,34)(23,37)(25,41)(26,40)(27,42)(29,46)(30,45)(31,35)(36,44)(38,47)(39,43)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2327);