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×#24410 |
| 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 | |
1322 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)(10,18,21,14)(11,23,24,15)(12,17)(13,16)(19,26,30,22)(20,29)(25,36,37,31)(27,28)(32,35)(33,38)(34,39);(8,10,13,21)(9,14,16,18)(11,20,24,35)(12,26,28,22)(15,29,23,32)(17,19,27,30)(25,38,37,34)(31,33,36,39);(8,9)(10,19)(11,15)(12,27)(13,16)(14,26)(17,28)(18,22)(20,33)(21,30)(23,24)(25,36)(29,38)(31,37)(32,34)(35,39);(8,11)(9,15)(10,20)(12,25)(13,24)(14,29)(16,23)(17,31)(18,32)(19,33)(21,35)(22,34)(26,38)(27,36)(28,37)(30,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17398);