Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C22×C43 |
| direct product | C7×#14651 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator | C23 | C23×C4×C7 |
| Frattini, cosocle | C24 | C24×C7 |
| prime radical | C2×C7×#392 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
1810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,10,11)(13,16)(17,19)(28,29,31,32)(30,33,35,34);(13,16)(14,18)(21,24)(25,27)(29,32)(33,34);(12,13)(14,17)(15,16)(18,19)(20,21)(22,25)(23,24)(26,27)(28,29)(30,34)(31,32)(33,35);(12,14)(13,17)(15,18)(16,19)(20,22,23,26)(21,25,24,27)(28,30)(29,33)(31,35)(32,34)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 7639);