Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C23×C4 |
| direct product | C7×#19726 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C7×#3184 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
724 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)(8,9,14,11)(10,17,21,23)(12,16,13,22)(15,19,18,20)(24,25,30,35)(26,32,37,38)(27,31,36,39)(28,33,29,34);(8,10,12,19,14,21,13,20)(9,15,22,23,11,18,16,17)(24,26,29,36,30,37,28,27)(25,31,33,38,35,39,34,32);(8,11,14,9)(10,18,21,15)(12,16,13,22)(17,20,23,19)(24,27,28,37,30,36,29,26)(25,32,34,39,35,38,33,31);(8,12,14,13)(9,16,11,22)(10,19,21,20)(15,17,18,23)(24,28,30,29)(25,33,35,34)(26,36,37,27)(31,32,39,38)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12714);