Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9946 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#9959 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
568 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,17)(10,18,20,22)(11,14,12,16)(15,21,23,19)(24,25)(26,29)(27,30)(28,31)(32,35)(33,36)(34,38)(37,39);(9,14)(11,12)(15,18)(16,17)(19,21)(22,23)(24,26,28,33)(25,29,31,36)(27,32,34,39)(30,37,38,35);(8,10,13,20)(9,15,17,23)(11,19,12,21)(14,22,16,18)(24,27)(25,30)(26,32)(28,34)(29,35)(31,38)(33,39)(36,37)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2947);