Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23874 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1674 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)(10,15)(11,22)(12,14)(13,18)(16,23)(17,25)(19,34)(20,29)(21,31)(24,33)(26,28)(27,32)(30,35)(36,38)(37,39);(9,14)(12,25)(15,29)(16,22)(17,18)(20,26)(23,27)(28,31)(30,34)(32,33)(35,37)(38,39);(8,10,13,21)(9,15,18,31)(11,19,24,36)(12,26,25,20)(14,28,17,29)(16,30,32,39)(22,38,33,34)(23,37,27,35);(8,11)(9,16)(10,19)(12,27)(13,24)(14,22)(15,30)(17,33)(18,32)(20,37)(21,36)(23,25)(26,35)(28,38)(29,34)(31,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16862);