Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#36699 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| socle | C23×C7 | C25 |
| prime radical | C2×C7×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ G | |
1958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7)(8,9,10,11)(12,13)(14,18)(15,19)(16,17)(20,23)(21,25)(22,24)(26,27)(28,29,32,35)(30,33,37,41)(31,34,39,43)(36,40,38,42);(13,17)(18,23)(19,24)(25,27)(28,30,32,37)(29,33,35,41)(31,38,39,36)(34,42,43,40);(9,11)(12,14)(13,18)(15,21)(16,20)(17,23)(19,25)(22,26)(24,27)(28,31)(29,34)(30,36)(32,39)(33,40)(35,43)(37,38)(41,42);(14,20)(18,23)(21,26)(25,27)(29,35)(31,39)(33,41)(36,38);(12,15,16,22)(13,19,17,24)(14,21,20,26)(18,25,23,27)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 29687);