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×#23889 |
| 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 | |
1648 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)(14,24)(15,29)(16,23)(17,22)(18,27)(19,31)(20,30)(21,34)(25,40)(26,35)(28,37)(32,39)(33,36)(38,42)(41,43);(12,14,17,28)(13,18,22,36)(15,26,31,41)(16,33,34,27)(19,38,29,40)(20,35,39,43)(21,37,23,24)(25,30,42,32);(9,11)(12,15)(13,19)(14,25)(16,30)(17,31)(18,35)(20,21)(22,29)(23,39)(24,38)(26,33)(27,41)(28,42)(32,34)(36,43)(37,40);(12,15)(13,20)(14,26)(16,32)(17,31)(18,35)(19,21)(22,39)(23,29)(24,40)(25,33)(27,42)(28,41)(30,34)(36,43)(37,38)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16877);