Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#19209 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C23×C7 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
582 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,12,15)(10,16,18,23)(11,19,21,14)(13,20,22,17)(25,29)(26,33)(27,30)(32,37)(34,35)(36,39);(24,25,30,37,28,32,27,29)(26,31,33,39,34,38,35,36);(8,10,12,18)(9,13,15,22)(11,20,21,17)(14,23,19,16)(24,26,28,34)(25,31,32,38)(27,35,30,33)(29,36,37,39);(26,34)(31,38)(33,35)(36,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12197);