Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9914 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#9921 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G | |
672 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(13,17)(14,15)(18,19)(20,21)(22,25)(23,26)(24,27)(28,31)(29,32)(30,34)(33,35);(12,13,16,18)(14,17,15,19)(20,22,24,29)(21,25,27,32)(23,28,30,35)(26,33,34,31);(9,11)(12,14,16,15)(13,17,18,19)(20,23)(21,26)(22,28)(24,30)(25,31)(27,34)(29,35)(32,33)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2909);