Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27×C4 |
| direct product | C7×#60831 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
2014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7)(8,9)(10,14)(11,13)(12,15)(16,17)(18,27)(19,31)(20,26)(21,23)(22,35)(24,29)(25,33)(28,43)(30,39)(32,41)(34,40)(36,37)(38,44)(42,45)(46,47);(8,10,11,15)(9,12,13,14)(17,23)(24,37)(25,31)(26,35)(27,39)(38,47)(40,41)(42,43);(10,15)(12,14)(16,18,21,30)(17,24,23,37)(19,28,33,45)(20,29,22,36)(25,38,31,47)(26,39,35,27)(32,44,34,46)(40,42,41,43);(9,13)(12,14)(16,19)(17,25)(18,28)(20,34)(21,33)(22,32)(23,31)(24,38)(26,41)(27,42)(29,46)(30,45)(35,40)(36,44)(37,47)(39,43);(16,20,21,22)(17,26,23,35)(18,29,30,36)(19,32,33,34)(24,39,37,27)(25,40,31,41)(28,44,45,46)(38,42,47,43)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53819);