Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23918 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#24010 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C25×C7 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C24×C4×C7 ◁ G | |
1428 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(12,13)(14,17)(15,16)(18,19)(20,21,25,28)(22,26,24,32)(23,30,31,34)(27,33,35,29);(8,9)(10,11)(13,16)(17,19)(20,22,25,24)(21,26,28,32)(23,29,31,33)(27,34,35,30);(9,11)(12,14,15,18)(13,17,16,19)(20,23)(21,27)(22,29)(24,33)(25,31)(26,34)(28,35)(30,32);(13,16)(17,19)(20,22,25,24)(21,26,28,32)(23,29,31,33)(27,34,35,30)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16998);