Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23916 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3487 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1694 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)(12,13,17,21)(14,22,24,36)(15,19,26,34)(16,28,29,20)(18,30,33,25)(23,39,40,38)(27,37,31,35)(32,42,43,41);(8,9)(10,11)(15,26)(16,29)(19,34)(20,28)(22,36)(23,40)(25,30)(32,43);(9,11)(12,14)(13,18)(15,23)(16,30)(17,24)(19,32)(20,36)(21,33)(22,28)(25,29)(26,40)(27,42)(31,41)(34,43)(35,38)(37,39);(12,15,17,26)(13,19,21,34)(14,23,24,40)(16,31,29,27)(18,32,33,43)(20,37,28,35)(22,38,36,39)(25,42,30,41)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16904);