Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1418 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C2×C7×#1419 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #357 |
| commutator | C16 | C22×C4×C7 |
| Frattini, cosocle | C2×C16 | C23×C7 |
| prime radical | C22×C7×D16 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C22×C7×C8 ◁ C22×C7×C16 ◁ G | |
326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2)(35,36,37,38,39,40,41);(3,4,6,12,9,14,8,25)(5,15,18,32,21,10,20,26)(7,22,17,29,24,30,23,13)(11,28,27,16,31,34,33,19);(4,10)(5,16)(6,8)(7,23)(11,29)(12,32)(13,31)(14,15)(17,24)(18,28)(19,21)(20,34)(22,27)(25,26)(30,33)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6611);