Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23998 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23999 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,18)(11,15)(12,25)(13,17)(14,22)(16,28)(19,26)(20,36)(21,32)(23,33)(24,31)(27,30)(29,38)(34,37)(35,39);(8,9)(10,19,21,14)(11,15)(12,16)(13,17)(18,22,32,26)(20,35,37,29)(23,30)(24,31)(25,28)(27,33)(34,39,36,38);(8,10)(9,14)(11,20)(12,26)(13,21)(15,29)(16,32)(17,19)(18,25)(22,28)(23,39)(24,37)(27,38)(30,34)(31,35)(33,36);(8,11,13,24)(9,15,17,31)(10,20,21,37)(12,27,28,23)(14,29,19,35)(16,33,25,30)(18,34,32,36)(22,39,26,38)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16987);