Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24473 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1314 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)(8,9,14,18,15,12,13,30)(10,19,22,16,24,33,23,21)(11,25,28,27,29,35,31,17)(20,37,38,34,39,32,26,36);(8,10)(9,16)(11,26)(12,21)(13,23)(14,22)(15,24)(17,34)(18,33)(19,30)(20,28)(25,32)(27,36)(29,38)(31,39)(35,37);(8,11)(9,17)(10,20)(12,27)(13,28)(14,31)(15,29)(16,32)(18,35)(19,36)(21,37)(22,26)(23,38)(24,39)(25,30)(33,34);(8,12,15,9)(10,21,24,16)(11,27,29,17)(13,18,14,30)(19,23,33,22)(20,37,39,32)(25,28,35,31)(26,36,38,34)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17461);