Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23994 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24285 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #535 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | #2408 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C4×C7 ◁ G | |
1336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18)(11,22)(12,25)(13,17)(14,20)(15,23)(16,26)(19,32)(21,30)(24,36)(27,35)(28,34)(29,37)(31,33)(38,39);(8,10,12,20,13,21,26,35)(9,14,16,18,17,27,25,30)(11,19,23,33,24,34,37,39)(15,28,22,31,29,32,36,38);(14,27)(18,30)(28,32)(31,38);(8,11,12,23,13,24,26,37)(9,15,16,22,17,29,25,36)(10,19,20,33,21,34,35,39)(14,28,18,31,27,32,30,38)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17273);