Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#13336 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C7×#405 ◁ G | |
586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(12,13)(14,25)(15,19)(16,32)(17,35)(18,24)(20,27)(21,29)(22,33)(23,31)(26,38)(28,37)(30,39)(34,42)(36,41)(40,43);(8,9)(10,11)(13,19)(14,26)(15,29)(16,33)(17,31)(20,38)(21,23)(22,35)(24,32)(25,42)(27,43)(28,36)(37,39)(40,41);(9,11)(12,14)(13,20)(15,30)(16,34)(17,36)(18,28)(19,37)(21,38)(22,41)(23,42)(24,40)(25,32)(26,31)(27,33)(29,43)(35,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6324);