Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23444 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23446 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C7×#3449 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1994 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)(14,18)(15,19)(16,20)(17,21)(22,29)(23,30)(24,31)(25,33)(26,34)(27,35)(28,36)(32,38)(37,41)(39,42)(40,43);(12,14,17,24)(13,18,21,31)(15,22,26,38)(16,27,28,23)(19,32,34,29)(20,35,36,30)(25,39,40,37)(33,41,43,42);(9,11)(12,15)(13,19)(14,22)(16,25)(17,26)(18,29)(20,33)(21,34)(23,37)(24,38)(27,39)(28,40)(30,41)(31,32)(35,42)(36,43);(12,16,17,28)(13,20,21,36)(14,23,24,27)(15,25,26,40)(18,30,31,35)(19,33,34,43)(22,37,38,39)(29,41,32,42)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16434);