Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27×C4 |
| direct product | C7×#60835 |
| 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 | |
2040 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)(16,17,20,25)(18,27,28,22)(19,31,32,24)(21,23,34,26)(29,36,41,40)(30,35,42,37)(33,39,44,38)(43,46,47,45);(8,10,11,15)(9,12,13,14)(16,18)(17,22)(19,29)(20,28)(21,30)(23,37)(24,36)(25,27)(26,35)(31,40)(32,41)(33,43)(34,42)(38,46)(39,45)(44,47);(10,15)(12,14)(17,23)(18,28)(21,34)(22,35)(24,38)(25,26)(27,37)(29,41)(31,39)(33,44)(36,45)(40,46);(9,13)(12,14)(16,19)(17,24)(18,29)(20,32)(21,33)(22,36)(23,38)(25,31)(26,39)(27,40)(28,41)(30,43)(34,44)(35,45)(37,46)(42,47);(18,28)(19,32)(22,27)(24,31)(30,42)(33,44)(35,37)(38,39)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53823);