Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7×C8 · Schur multiplier (H2) = C26 |
| direct product | C7×#17351 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C22×C22⋊C4 |
| commutator | C22 | C23×C7×C8 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#41 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C4×C7×D4 ◁ G | |
1278 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9,10,12,11,13,14,15)(16,17)(18,24,26,21)(19,22)(20,23)(25,30,31,28)(27,29);(16,18,20,26)(17,21,23,24)(19,25,27,31)(22,28,29,30);(16,19)(17,22)(18,25)(20,27)(21,28)(23,29)(24,30)(26,31);(19,27)(22,29)(25,31)(28,30)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 10339);