Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C214 |
| direct product | C7×#62848 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ G | |
10962 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 6 generators on 43 points:
(1,2,3,4,5,6,7)(9,11)(13,18)(16,28)(19,22)(20,29)(24,38)(27,39)(31,34)(37,43);(8,9)(10,11)(15,26)(20,29)(23,36)(27,39)(31,34)(33,40)(37,43)(41,42);(12,13,17,18)(14,22,25,19)(15,20,26,29)(16,21,28,30)(23,34,36,31)(24,35,38,32)(27,33,39,40)(37,42,43,41);(12,14,17,25)(13,19,18,22)(15,23,26,36)(16,24,28,38)(20,31,29,34)(21,32,30,35)(27,37,39,43)(33,41,40,42);(12,15)(13,20)(14,23)(16,27)(17,26)(18,29)(19,31)(21,33)(22,34)(24,37)(25,36)(28,39)(30,40)(32,41)(35,42)(38,43);(12,16)(13,21)(14,24)(15,27)(17,28)(18,30)(19,32)(20,33)(22,35)(23,37)(25,38)(26,39)(29,40)(31,41)(34,42)(36,43)574 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55836);