Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25142 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,16,20,17,21,30,37)(14,18,23,32,24,33,41,43)(15,25,27,35,28,36,29,19)(22,38,39,34,26,42,40,31);(9,11)(12,14,16,23,17,24,30,41)(13,18,20,32,21,33,37,43)(15,26,27,40,28,22,29,39)(19,34,25,42,35,31,36,38);(12,15,17,28)(13,19,21,35)(14,22,24,26)(16,29,30,27)(18,31,33,34)(20,36,37,25)(23,40,41,39)(32,42,43,38);(9,11)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18130);