Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23891 |
| 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 | |
1622 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)(12,13,17,22)(14,23,27,24)(15,29,31,37)(16,32,18,21)(19,28,35,26)(20,33,36,30)(25,34,41,43)(38,42,39,40);(12,14,17,27)(13,19,22,35)(15,25,31,41)(16,28,18,26)(20,34,36,43)(21,24,32,23)(29,38,37,39)(30,42,33,40);(9,11)(12,13)(14,24)(15,20)(16,21)(17,22)(18,32)(19,26)(23,27)(25,39)(28,35)(29,30)(31,36)(33,37)(34,42)(38,41)(40,43);(12,15,17,31)(13,20,22,36)(14,25,27,41)(16,33,18,30)(19,34,35,43)(21,37,32,29)(23,38,24,39)(26,42,28,40)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16879);