Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#23639 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C7×#41 ◁ G | |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
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)(20,21,23,27,24,28,31,26)(22,25,30,34,29,33,35,32);(8,9)(10,11)(13,16)(17,19)(20,22)(21,25)(23,30)(24,29)(26,32)(27,34)(28,33)(31,35);(9,11)(12,14,15,18)(13,17,16,19)(21,26)(23,31)(25,32)(27,28)(30,35)(33,34);(22,29)(25,33)(30,35)(32,34)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16627);