Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#19215 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C23×C7 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
582 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9)(10,16)(11,13)(12,20)(14,18)(15,19)(17,23)(21,22)(24,25,29,32)(26,33,31,28)(27,34,35,39)(30,36,38,37);(9,13)(14,22)(15,20)(16,23)(24,26,28,25,29,31,33,32)(27,34,36,30,35,39,37,38);(8,10,11,17)(9,14,13,22)(12,21,19,18)(15,23,20,16)(24,27,29,35)(25,30,32,38)(26,34,31,39)(28,36,33,37);(27,35)(30,38)(34,39)(36,37)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12203);