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×#24287 |
| 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 | |
1298 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)(10,22)(11,26)(12,30)(13,20)(14,19)(15,21)(16,24)(17,28)(18,27)(23,34)(25,39)(29,35)(31,38)(32,36)(33,37);(8,10,13,24,15,25,14,32)(9,16,19,22,21,36,20,39)(11,27,28,31,29,23,33,12)(17,34,26,38,37,18,35,30);(8,11)(9,17)(10,23)(12,24)(13,28)(14,33)(15,29)(16,34)(18,36)(19,26)(20,35)(21,37)(22,38)(25,27)(30,39)(31,32);(8,12,13,27,15,31,14,23)(9,18,19,30,21,34,20,38)(10,11,24,28,25,29,32,33)(16,35,22,17,36,26,39,37)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17275);