Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25198 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3020 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
958 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)(8,9,12,17,13,18,28,16)(10,19,22,30,23,32,21,14)(11,24,26,31,27,33,25,15)(20,29,35,38,36,39,37,34);(8,10,12,22,13,23,28,21)(9,14,17,19,18,30,16,32)(11,20,26,35,27,36,25,37)(15,29,24,38,31,39,33,34);(8,11,13,27)(9,15,18,31)(10,20,23,36)(12,25,28,26)(14,29,30,39)(16,24,17,33)(19,34,32,38)(21,35,22,37);(8,9)(10,14)(11,15)(12,17)(13,18)(16,28)(19,22)(20,29)(21,32)(23,30)(24,26)(25,33)(27,31)(34,37)(35,38)(36,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18186);