Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60372 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60524 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#3489 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C7×#41 ◁ G | |
2116 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)(10,13)(11,12)(14,15)(16,17,21,26)(18,22,29,36)(19,24,30,38)(20,23,32,25)(27,34,40,45)(28,33,42,35)(31,37,43,39)(41,44,47,46);(9,12)(13,15)(16,18,21,29)(17,22,26,36)(19,27,30,40)(20,28,32,42)(23,33,25,35)(24,34,38,45)(31,41,43,47)(37,44,39,46);(8,10,11,14)(9,13,12,15)(17,23)(20,32)(22,33)(24,37)(25,26)(28,42)(31,43)(34,44)(35,36)(38,39)(41,47)(45,46);(16,19)(17,24)(18,27)(20,31)(21,30)(22,34)(23,37)(25,39)(26,38)(28,41)(29,40)(32,43)(33,44)(35,46)(36,45)(42,47);(19,30)(24,38)(27,40)(31,43)(34,45)(37,39)(41,47)(44,46)427 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53512);