Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2018 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23438 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C7 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C22×C7 | C2×#121 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C7 ◁ C23×C4×C7 ◁ G | |
1922 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)(14,24)(15,29)(16,21)(17,22)(18,23)(19,27)(20,32)(25,40)(26,36)(28,35)(30,37)(31,39)(33,38)(34,42)(41,43);(9,11)(12,14)(13,19)(15,30)(16,26)(17,27)(18,28)(20,37)(21,24)(22,35)(23,36)(25,31)(29,40)(32,42)(33,41)(34,38)(39,43);(12,15)(13,20)(14,25)(16,31)(17,32)(18,33)(19,34)(21,29)(22,38)(23,39)(24,37)(26,41)(27,30)(28,42)(35,43)(36,40);(12,16,18,17)(13,21,23,22)(14,26,28,27)(15,31,33,32)(19,24,36,35)(20,29,39,38)(25,41,42,30)(34,37,40,43)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16426);