Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24297 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1334 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)(8,9,15,18)(10,13,21,14)(11,22,26,19)(12,20,29,34)(16,24,31,25)(17,28,32,27)(23,30,38,39)(33,36,35,37);(8,10,13,18,15,21,14,9)(11,16,24,19,26,31,25,22)(12,20,27,32,29,34,28,17)(23,30,36,33,38,39,37,35);(8,11)(9,16)(10,19)(12,23)(13,24)(14,25)(15,26)(17,30)(18,31)(20,33)(21,22)(27,36)(28,37)(29,38)(32,39)(34,35);(8,12,14,28,15,29,13,27)(9,17,21,34,18,32,10,20)(11,23,25,37,26,38,24,36)(16,30,22,35,31,39,19,33)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17285);