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×#60828 |
| 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 | |
2018 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 448 |
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)(18,26)(19,30)(20,22)(21,34)(23,29)(24,31)(25,33)(27,41)(28,39)(32,38)(35,36)(37,47)(40,42)(43,44)(45,46);(8,10,11,15)(9,12,13,14)(17,22)(23,36)(24,30)(25,34)(26,39)(37,44)(38,45)(40,41);(10,15)(12,14)(16,18,20,28)(17,23,22,36)(19,27,31,42)(21,35,33,29)(24,37,30,44)(25,39,34,26)(32,47,46,43)(38,41,45,40);(9,13)(12,14)(16,19)(17,24)(18,27)(20,31)(21,32)(22,30)(23,37)(25,38)(26,40)(28,42)(29,43)(33,46)(34,45)(35,47)(36,44)(39,41);(19,31)(24,30)(27,42)(32,46)(37,44)(38,45)(40,41)(43,47)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53816);