Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23897 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23898 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1718 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)(10,14)(11,21)(12,24)(13,17)(15,23)(16,26)(18,33)(19,36)(20,29)(22,32)(25,31)(27,35)(28,38)(30,37)(34,39);(8,10,13,20)(9,14,17,29)(11,18,22,34)(12,19,26,38)(15,30,31,27)(16,28,24,36)(21,39,32,33)(23,35,25,37);(8,11)(9,15)(10,18)(12,25)(13,22)(14,27)(16,32)(17,31)(19,37)(20,34)(21,24)(23,26)(28,39)(29,30)(33,36)(35,38);(12,26)(16,24)(19,38)(21,32)(23,25)(28,36)(33,39)(35,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16886);