Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24295 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1302 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)(10,12)(11,24)(13,32)(14,19)(15,20)(16,22)(17,28)(18,30)(21,33)(23,31)(25,26)(27,35)(29,34)(36,39)(37,38);(8,10,13,22,15,23,14,18)(9,16,19,12,20,30,32,31)(11,25,27,21,29,36,28,37)(17,26,34,38,35,39,24,33);(8,11)(9,17)(10,21)(12,26)(13,27)(14,28)(15,29)(16,33)(18,25)(19,34)(20,35)(22,36)(23,37)(24,32)(30,38)(31,39);(8,12,13,30,15,31,14,16)(9,18,19,10,20,22,32,23)(11,26,27,38,29,39,28,33)(17,25,34,21,35,36,24,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17283);