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×#23527 |
| 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 | |
1336 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)(11,22)(12,26)(13,17)(14,20)(15,24)(16,28)(19,33)(21,32)(23,37)(25,31)(27,30)(29,34)(35,38)(36,39);(8,10)(9,14)(11,23)(12,27)(13,21)(15,29)(16,32)(17,30)(18,26)(19,24)(20,28)(22,35)(25,34)(31,37)(33,36)(38,39);(8,11,12,25,13,24,28,39)(9,15,16,31,17,22,26,36)(10,19,20,34,21,23,27,38)(14,29,18,33,30,35,32,37);(11,24)(15,22)(19,23)(25,39)(29,35)(31,36)(33,37)(34,38)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16515);