Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×#60462 |
| 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 ◁ C22×C7×#41 ◁ G | |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,17,21)(14,22,24,35)(15,19,27,33)(16,29,23,20)(18,30,31,26)(25,36,38,43)(28,40,37,34)(32,41,42,39);(12,14,23,30,17,24,16,26)(13,18,29,35,21,31,20,22)(15,25,37,41,27,38,28,39)(19,32,40,43,33,42,34,36);(9,11)(14,24)(18,31)(22,35)(25,38)(26,30)(32,42)(36,43)(39,41);(12,15)(13,19)(14,25)(16,28)(17,27)(18,32)(20,34)(21,33)(22,36)(23,37)(24,38)(26,39)(29,40)(30,41)(31,42)(35,43);(15,27)(19,33)(25,38)(28,37)(32,42)(34,40)(36,43)(39,41)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53450);