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×#23885 |
| 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 | |
1662 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)(10,21)(11,26)(12,29)(13,19)(14,18)(15,20)(16,24)(17,28)(22,31)(23,32)(25,35)(27,34)(30,33)(36,38)(37,39);(8,10)(9,16)(11,22)(12,23)(13,30)(14,24)(15,25)(17,32)(18,35)(19,21)(20,33)(26,36)(27,39)(28,38)(29,37)(31,34);(8,11,15,12)(9,17,20,34)(10,22,25,23)(13,28,14,27)(16,31,33,32)(18,26,19,29)(21,36,35,37)(24,39,30,38);(8,12,15,11)(9,17,20,34)(10,23,25,22)(13,27,14,28)(16,32,33,31)(18,26,19,29)(21,37,35,36)(24,38,30,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16873);