Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60470 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×#60471 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | C22×#121 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C7×#41 ◁ G | |
2630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2,3,4,5,6,7)(9,14)(10,19)(12,15)(17,26)(18,27)(20,33)(21,22)(24,28)(25,30)(32,37)(34,35)(36,39);(8,9,15,27,13,18,12,14)(10,16,19,30,22,31,21,25)(11,17,28,37,23,32,24,26)(20,29,33,39,34,38,35,36);(8,10)(9,16)(11,20)(12,21)(13,22)(14,25)(15,19)(17,29)(18,31)(23,34)(24,35)(26,36)(27,30)(28,33)(32,38)(37,39);(8,11)(9,17)(10,20)(12,24)(13,23)(14,26)(15,28)(16,29)(18,32)(19,33)(21,35)(22,34)(25,36)(27,37)(30,39)(31,38);(11,23)(17,32)(20,34)(24,28)(26,37)(29,38)(33,35)(36,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53459);