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×#25143 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C7×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
996 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)(12,13,17,22,18,23,16,21)(14,19,26,35,27,36,25,34)(15,28,30,38,31,39,32,20)(24,40,41,37,29,43,42,33);(9,11)(12,14,17,26,18,27,16,25)(13,19,22,35,23,36,21,34)(15,29,30,42,31,24,32,41)(20,37,28,43,38,33,39,40);(12,15,18,31)(13,20,23,38)(14,24,27,29)(16,30,17,32)(19,33,36,37)(21,28,22,39)(25,41,26,42)(34,40,35,43);(9,11)(12,16,18,17)(13,21,23,22)(14,25,27,26)(15,30,31,32)(19,34,36,35)(20,28,38,39)(24,41,29,42)(33,40,37,43)301 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18131);