Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#24420 |
| 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 | |
1326 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)(8,9,12,18,14,15,13,19)(10,20,24,29,23,31,21,16)(11,25,26,33,27,17,28,32)(22,34,35,30,36,39,37,38);(9,15)(10,21)(12,13)(16,20)(17,25)(22,35)(23,24)(26,28)(29,31)(30,34)(36,37)(38,39);(8,10)(9,16)(11,22)(12,21)(13,24)(14,23)(15,29)(17,30)(18,31)(19,20)(25,38)(26,37)(27,36)(28,35)(32,34)(33,39);(8,11)(9,17)(10,22)(12,28)(13,26)(14,27)(15,25)(16,30)(18,33)(19,32)(20,34)(21,35)(23,36)(24,37)(29,38)(31,39)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17408);