Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#22887 |
| 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 | C7×#3002 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C2×C7×C22⋊C8 ◁ G | |
1020 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)(8,9)(10,11)(12,13,17,21,18,22,16,30)(14,23,25,19,26,34,31,35)(15,20,29,39,28,37,32,38)(24,40,42,33,41,36,27,43);(12,14,17,25,18,26,16,31)(13,19,21,34,22,35,30,23)(15,27,29,24,28,42,32,41)(20,36,39,43,37,40,38,33);(9,11)(15,28)(20,37)(24,41)(27,42)(29,32)(33,43)(36,40)(38,39);(12,15)(13,20)(14,24)(16,32)(17,29)(18,28)(19,33)(21,39)(22,37)(23,40)(25,42)(26,41)(27,31)(30,38)(34,36)(35,43)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15875);