Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32870 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#32870 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2826 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#2018 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
502 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)(8,9,12,16,14,19,13,18)(10,20,23,15,24,30,21,31)(11,17,27,32,28,33,26,34)(22,35,37,29,25,38,36,39);(8,10,12,23,14,24,13,21)(9,15,18,20,19,31,16,30)(11,25,26,37,28,22,27,36)(17,29,32,38,33,39,34,35);(9,16)(10,21)(11,26)(12,13)(17,33)(18,19)(20,30)(22,25)(23,24)(27,28)(29,38)(35,39);(8,11)(9,17)(10,22)(12,27)(13,26)(14,28)(15,29)(16,32)(18,34)(19,33)(20,35)(21,36)(23,37)(24,25)(30,38)(31,39)196 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 25858);