Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28×C4 |
| direct product | C7×#60648 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
3114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7)(9,11)(12,13,17,21)(14,22,26,36)(15,19,27,33)(16,29,23,20)(18,30,32,25)(24,35,38,43)(28,40,37,34)(31,41,42,39);(12,14,23,30,17,26,16,25)(13,18,29,36,21,32,20,22)(15,24,37,41,27,38,28,39)(19,31,40,43,33,42,34,35);(8,9,10,11);(12,15)(13,19)(14,24)(16,28)(17,27)(18,31)(20,34)(21,33)(22,35)(23,37)(25,39)(26,38)(29,40)(30,41)(32,42)(36,43);(15,27)(19,33)(24,38)(28,37)(31,42)(34,40)(35,43)(39,41)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53636);