Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9103 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#10990 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,17,21,18,22,16,31)(14,23,25,19,26,35,32,34)(15,27,29,38,30,20,28,37)(24,40,41,33,42,39,43,36);(12,14)(13,19)(15,24)(16,32)(17,25)(18,26)(20,36)(21,35)(22,34)(23,31)(27,33)(28,43)(29,41)(30,42)(37,40)(38,39);(9,11)(12,15,18,30)(13,20,22,27)(14,24,26,42)(16,29,17,28)(19,33,34,36)(21,38,31,37)(23,39,35,40)(25,43,32,41)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 3978);