Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23882 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23884 |
| 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 | |
1684 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)(10,20)(11,24)(12,18)(13,16)(14,19)(15,22)(17,25)(21,29)(23,31)(26,33)(27,32)(28,30)(34,35)(36,39)(37,38);(8,10)(9,15)(11,21)(12,28)(13,22)(14,23)(16,31)(17,29)(18,20)(19,30)(24,34)(25,37)(26,35)(27,36)(32,38)(33,39);(9,16)(12,13)(15,20)(17,32)(18,19)(22,28)(24,33)(25,26)(29,34)(30,31)(35,37)(38,39);(8,11,14,27)(9,17,19,33)(10,21,23,36)(12,26,13,25)(15,29,30,39)(16,32,18,24)(20,34,31,38)(22,37,28,35)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16872);