Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1942 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)(14,23)(15,20)(16,21)(17,30)(18,22)(19,25)(24,39)(26,33)(27,36)(28,38)(29,37)(31,34)(32,42)(35,40)(41,43);(12,14)(13,19)(15,24)(16,25)(17,31)(18,26)(20,35)(21,33)(22,34)(23,30)(27,40)(28,42)(29,41)(32,37)(36,43)(38,39);(9,11)(12,15,18,29)(13,20,22,37)(14,24,26,41)(16,28,17,27)(19,32,34,35)(21,38,30,36)(23,39,33,43)(25,42,31,40);(12,16,18,17)(13,21,22,30)(14,25,26,31)(15,27,29,28)(19,33,34,23)(20,36,37,38)(24,40,41,42)(32,39,35,43)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16391);