Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#20917 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×C4×D4 |
| prime radical | C2×C7×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C7×C8 ◁ G | |
1698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(9,11)(12,13)(14,24,28,35)(15,29,32,37)(16,22)(17,23)(18,21)(19,26,34,27)(20,31,36,30)(25,39)(33,42)(38,40)(41,43);(8,9,10,11)(12,14,16,27,18,28,17,26)(13,19,22,35,21,34,23,24)(15,25,31,40,32,42,30,41)(20,33,29,43,36,39,37,38);(12,15)(13,20)(14,25)(16,31)(17,30)(18,32)(19,33)(21,36)(22,29)(23,37)(24,38)(26,41)(27,40)(28,42)(34,39)(35,43);(13,21)(19,34)(20,36)(22,23)(24,35)(29,37)(33,39)(38,43)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 13905);