Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24408 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24408 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1364 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)(10,18,20,14)(11,15)(12,17)(13,16)(19,28,37,36)(21,34,25,29)(22,30,38,39)(23,32)(24,31)(26,35)(27,33);(8,10)(9,14)(11,22)(12,25)(13,20)(15,30)(16,18)(17,34)(19,24)(21,27)(23,38)(26,37)(28,31)(29,33)(32,39)(35,36);(8,11)(9,15)(10,19)(12,26)(13,23)(14,28)(16,32)(17,35)(18,36)(20,37)(21,38)(22,25)(24,27)(29,39)(30,34)(31,33);(8,10)(9,14)(11,19)(12,21)(13,20)(15,28)(16,18)(17,29)(22,24)(23,37)(25,27)(26,38)(30,31)(32,36)(33,34)(35,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17396);