Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#11265 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #388 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle | C2×C7 | #1442 |
| prime radical | C24×C7 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,20)(11,25,29,33)(12,18)(13,17)(14,19)(15,22)(16,27,34,28)(21,36,38,30)(23,31)(24,35)(26,39,37,32);(8,10,12,23,14,24,13,22)(9,15,18,20,19,31,17,35)(11,26,27,38,29,37,28,21)(16,32,25,36,34,39,33,30);(8,11,12,27,14,29,13,28)(9,16,17,33,19,34,18,25)(10,21,22,37,24,38,23,26)(15,30,20,32,31,36,35,39)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4253);