Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23990 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23993 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3021 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1152 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)(8,9,12,14)(10,15,20,27)(11,21,22,16)(13,25,24,17)(18,28,26,30)(19,29,33,34)(23,31,36,35)(32,38,37,39);(9,14)(10,18,20,26)(15,28,27,30)(16,21)(17,25)(19,32,33,37)(29,38,34,39)(31,35);(8,10)(9,15)(11,19)(12,20)(13,26)(14,27)(16,29)(17,28)(18,24)(21,34)(22,33)(23,37)(25,30)(31,38)(32,36)(35,39);(8,11)(9,16)(10,19)(12,22)(13,23)(14,21)(15,29)(17,31)(18,32)(20,33)(24,36)(25,35)(26,37)(27,34)(28,38)(30,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16981);