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×#60470 |
| 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 | |
2604 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)(10,18)(12,24)(16,26)(17,27)(19,32)(20,21)(23,35)(25,29)(31,37)(33,34)(36,39);(8,9,12,14,13,17,24,27)(10,15,20,25,21,30,18,29)(11,16,23,26,22,31,35,37)(19,28,34,36,33,38,32,39);(8,10)(9,15)(11,19)(12,20)(13,21)(14,25)(16,28)(17,30)(18,24)(22,33)(23,34)(26,36)(27,29)(31,38)(32,35)(37,39);(8,11)(9,16)(10,19)(12,23)(13,22)(14,26)(15,28)(17,31)(18,32)(20,34)(21,33)(24,35)(25,36)(27,37)(29,39)(30,38);(11,22)(16,31)(19,33)(23,35)(26,37)(28,38)(32,34)(36,39)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53458);