Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24986 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#24986 |
| 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 | |
642 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)(10,21)(11,25)(12,16)(13,30)(14,19)(15,20)(17,28)(18,24)(22,31)(23,32)(26,33)(27,35)(29,34)(36,37)(38,39);(8,10,13,12,15,24,14,23)(9,16,19,21,20,32,30,18)(11,26,28,22,29,37,27,38)(17,33,25,39,35,36,34,31);(8,11)(9,17)(10,22)(12,26)(13,27)(14,28)(15,29)(16,31)(18,33)(19,34)(20,35)(21,36)(23,37)(24,38)(25,30)(32,39);(8,12,13,24,15,23,14,10)(9,18,19,16,20,21,30,32)(11,26,27,38,29,37,28,22)(17,33,34,31,35,36,25,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17974);