Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24808 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2416 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3068 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
820 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)(8,9,12,17,13,18,28,16)(10,19,22,14,24,20,23,30)(11,25,26,15,27,31,39,32)(21,35,36,33,38,29,37,34);(8,10,12,22,13,24,28,23)(9,14,16,19,18,30,17,20)(11,21,26,36,27,38,39,37)(15,29,25,33,32,35,31,34);(8,9)(10,20)(11,15)(12,16)(13,18)(14,22)(17,28)(19,24)(21,34)(23,30)(25,26)(27,32)(29,36)(31,39)(33,38)(35,37);(8,11,12,26,13,27,28,39)(9,15,16,25,18,32,17,31)(10,21,22,36,24,38,23,37)(14,29,19,33,30,35,20,34)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17796);