Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13313 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#13394 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #466 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#41 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C7×#131 ◁ G | |
392 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(12,13,19,25)(14,26,29,38)(15,30,27,20)(16,24,18,22)(17,33,36,42)(21,39,41,31)(23,32,43,35)(28,40,34,37);(8,9)(10,11)(12,14)(13,20)(15,16)(17,34)(18,27)(19,29)(21,33)(22,38)(23,40)(24,26)(25,30)(28,36)(31,35)(32,39)(37,43)(41,42);(9,11)(12,15,16,14,19,27,18,29)(13,21,22,37,25,41,24,40)(17,34,32,31,36,28,35,39)(20,23,26,42,30,43,38,33)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6382);