Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#13455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C23×C7 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C7×#405 ◁ G | |
318 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,12,14)(10,15,11,13)(16,17)(18,22)(19,23)(20,25)(21,27)(24,32)(26,33)(28,41)(29,38)(30,36)(31,37)(34,40)(35,42)(39,45)(43,47)(44,46);(8,10,12,11)(9,13,14,15)(16,18)(17,22)(19,29)(20,28)(21,31)(23,38)(24,35)(25,41)(26,36)(27,37)(30,33)(32,42)(34,43)(39,46)(40,47)(44,45);(8,11,12,10)(9,13,14,15)(17,23)(18,28)(19,32)(20,33)(22,35)(24,26)(25,39)(27,40)(29,43)(30,31)(34,45)(36,47)(37,46)(38,41)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6443);