Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24985 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#24985 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | #2420 |
| prime radical | C7×#3067 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C4×C7 ◁ G | |
646 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)(12,16)(13,20)(14,19)(15,21)(17,29)(18,25)(23,38)(24,33)(27,35)(28,34)(30,36)(31,37)(32,39);(8,10,14,24,15,25,13,12)(9,16,20,18,21,33,19,22)(11,27,29,23,31,28,30,39)(17,34,26,38,36,35,37,32);(8,11)(9,17)(10,23)(12,28)(13,29)(14,30)(15,31)(16,32)(18,35)(19,26)(20,37)(21,36)(22,34)(24,27)(25,39)(33,38);(8,12,13,25,15,24,14,10)(9,18,19,16,21,22,20,33)(11,28,29,39,31,27,30,23)(17,35,26,32,36,34,37,38)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17973);