Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23535 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | C2×#394 |
| prime radical | C2×C7×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
1352 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)(10,19)(11,24)(12,29)(13,17)(14,18)(15,21)(16,27)(20,30)(22,32)(23,31)(25,33)(26,37)(28,34)(35,38)(36,39);(8,10)(9,15)(11,25)(12,22)(13,21)(14,23)(16,33)(17,31)(18,32)(19,29)(20,28)(24,30)(26,36)(27,35)(34,39)(37,38);(8,11,12,27,14,26,13,28)(9,16,17,24,18,34,29,37)(10,20,21,36,23,35,22,25)(15,30,19,33,32,38,31,39);(11,26)(16,34)(20,35)(24,37)(25,36)(27,28)(30,38)(33,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16523);