Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#21781 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2308 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3487 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1258 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)(8,9,13,19,14,18,11,16)(10,20,21,29,23,15,27,31)(12,25,24,33,26,17,28,32)(22,30,37,38,36,34,35,39);(8,10)(9,15)(11,21)(12,22)(13,27)(14,23)(16,31)(17,30)(18,20)(19,29)(24,35)(25,34)(26,36)(28,37)(32,39)(33,38);(8,11,14,13)(9,16,18,19)(10,21,23,27)(12,24,26,28)(15,29,20,31)(17,32,25,33)(22,35,36,37)(30,38,34,39);(8,12,14,26)(9,17,18,25)(10,22,23,36)(11,24,13,28)(15,30,20,34)(16,32,19,33)(21,35,27,37)(29,38,31,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14769);