Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#18452 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1028 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)(9,14)(10,18)(11,22)(15,28)(16,26)(17,23)(19,21)(20,35)(24,37)(27,32)(29,39)(30,36)(31,38)(33,34);(8,9,12,17)(10,15,19,29)(11,23,22,14)(13,16,25,31)(18,32,21,30)(20,36,34,27)(24,38,37,26)(28,33,39,35);(10,19)(11,24)(14,26)(15,29)(18,21)(20,33)(22,37)(23,38)(27,28)(30,32)(34,35)(36,39);(8,10,12,19)(9,15,17,29)(11,20,22,34)(13,21,25,18)(14,27,23,36)(16,30,31,32)(24,35,37,33)(26,39,38,28)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11440);