Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#18464 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
970 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)(9,14)(10,18)(11,23)(15,28)(16,26)(17,24)(19,22)(21,36)(25,35)(27,32)(29,39)(30,38)(31,37)(33,34);(8,9,12,17)(10,15,19,29)(11,24,23,14)(13,16,20,30)(18,32,22,31)(21,37,34,27)(25,38,35,26)(28,33,39,36);(10,19)(11,25)(14,26)(15,29)(18,22)(21,33)(23,35)(24,38)(27,28)(31,32)(34,36)(37,39);(8,10,20,18)(9,15,30,32)(11,21,35,33)(12,19,13,22)(14,27,38,28)(16,31,17,29)(23,34,25,36)(24,37,26,39)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 11452);