Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24290 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ G | |
1294 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)(8,9)(10,11)(12,13)(14,20)(15,28)(16,31)(17,24)(18,23)(19,26)(21,32)(22,29)(25,39)(27,35)(30,34)(33,38)(36,40)(37,43)(41,42);(12,14,17,26,18,15,29,27)(13,19,22,20,23,35,24,28)(16,25,32,40,33,30,43,41)(21,34,31,36,37,39,38,42);(9,11)(12,15)(13,20)(14,18)(16,30)(17,27)(19,24)(21,36)(22,35)(23,28)(25,33)(26,29)(31,39)(32,41)(34,38)(37,42)(40,43);(12,16,29,43,18,33,17,32)(13,21,24,38,23,37,22,31)(14,25,27,41,15,30,26,40)(19,34,28,42,35,39,20,36)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17278);