Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23525 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #394 |
| 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 | |
1332 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)(10,20)(11,25)(12,17)(13,18)(14,19)(15,23)(16,28)(21,32)(22,31)(24,35)(26,30)(27,34)(29,33)(36,38)(37,39);(8,10)(9,15)(11,26)(12,22)(13,23)(14,24)(16,32)(17,20)(18,35)(19,31)(21,29)(25,39)(27,38)(28,37)(30,34)(33,36);(8,11,12,27,14,29,13,28)(9,16,18,33,19,34,17,25)(10,21,23,38,24,26,22,37)(15,30,20,36,31,32,35,39);(8,12,14,13)(9,17,19,18)(10,22,24,23)(11,27,29,28)(15,20,31,35)(16,25,34,33)(21,37,26,38)(30,36,32,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16513);