Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25191 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3012 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(12,13,17,24,19,25,18,23)(14,26,30,40,31,39,29,20)(15,32,35,22,16,36,34,21)(27,37,28,38,43,42,33,41);(8,9)(10,11)(12,14,17,30,19,31,18,29)(13,20,24,26,25,40,23,39)(15,33,35,27,16,28,34,43)(21,41,32,37,22,38,36,42);(9,11)(12,15,19,16)(13,21,25,22)(14,27,31,43)(17,34,18,35)(20,37,40,42)(23,32,24,36)(26,41,39,38)(28,30,33,29);(12,16,19,15)(13,22,25,21)(14,28,31,33)(17,34,18,35)(20,38,40,41)(23,32,24,36)(26,42,39,37)(27,30,43,29)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18179);