Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23943 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
1158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7)(12,13)(14,18)(15,17)(16,19)(20,21,25,29)(22,26,31,40)(23,33,35,43)(24,36,38,28)(27,37,42,34)(30,44,45,51)(32,48,47,41)(39,49,50,46);(8,9)(10,11)(12,14,15,19)(13,16,17,18)(20,22)(21,26)(23,30)(24,32)(25,31)(27,39)(28,41)(29,40)(33,44)(34,46)(35,45)(36,48)(37,49)(38,47)(42,50)(43,51);(9,11)(20,23,25,35)(21,27,29,42)(22,30,31,45)(24,37,38,34)(26,39,40,50)(28,43,36,33)(32,49,47,46)(41,51,48,44);(13,17)(16,18)(22,31)(26,40)(30,45)(32,47)(39,50)(41,48)(44,51)(46,49)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16931);