Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#12930 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#106 |
| commutator | C2×C8 | C22×C4×C7 |
| Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C24×C7 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ C23×C7×C8 ◁ G | |
414 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)(12,13,15,19,17,22,29,21)(14,23,26,40,27,41,24,38)(16,30,28,20,32,37,42,39)(18,33,35,25,36,31,34,43);(12,14,17,27)(13,18)(15,24,29,26)(16,31,32,33)(19,34)(20,38)(21,35)(22,36)(23,30)(25,42,43,28)(37,41)(39,40);(9,11)(12,15,17,29)(13,19,22,21)(14,24,27,26)(16,28,32,42)(18,34,36,35)(20,37,39,30)(23,38,41,40)(25,33,43,31)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 5918);