Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23917 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
1682 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)(12,13)(14,19)(15,27)(16,21)(17,32)(18,23)(20,30)(22,25)(24,37)(26,36)(28,43)(29,39)(31,35)(33,38)(34,41)(40,42);(8,9)(10,11)(12,14,18,26)(13,19,23,36)(15,24,29,40)(16,17,31,25)(20,34,38,43)(21,32,35,22)(27,42,39,37)(28,33,41,30);(9,11)(12,15)(13,20)(14,24)(16,28)(17,33)(18,29)(19,34)(21,37)(22,39)(23,38)(25,30)(26,40)(27,32)(31,41)(35,42)(36,43);(12,16,18,31)(13,21,23,35)(14,25,26,17)(15,28,29,41)(19,22,36,32)(20,37,38,42)(24,30,40,33)(27,34,39,43)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16905);