Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×#60469 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#121 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| socle | C2×C7 | C22×#121 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
2628 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)(8,9)(10,20)(11,25)(12,17)(13,18)(14,19)(15,23)(16,26)(21,35)(22,31)(24,30)(27,32)(28,33)(29,36)(34,37)(38,39);(8,10,12,23,14,22,13,24)(9,15,18,20,19,30,17,31)(11,21,26,37,27,36,28,38)(16,29,25,34,33,35,32,39);(8,11)(9,16)(10,21)(12,26)(13,28)(14,27)(15,29)(17,32)(18,25)(19,33)(20,34)(22,36)(23,37)(24,38)(30,35)(31,39);(10,22)(15,30)(20,31)(21,36)(23,24)(29,35)(34,39)(37,38);(8,12,14,13)(9,17,19,18)(10,23,22,24)(11,26,27,28)(15,31,30,20)(16,32,33,25)(21,37,36,38)(29,39,35,34)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53457);