Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23924 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#24013 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#535 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C7×#41 ◁ G | |
1468 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)(22,25)(23,26)(24,28)(27,31)(29,33)(30,32)(34,35);(8,9)(10,11)(13,16)(17,19)(20,22,24,29)(21,25,28,33)(23,30,31,35)(26,32,27,34);(9,11)(12,14,15,18)(13,17,16,19)(21,26)(23,31)(25,32)(27,28)(30,35)(33,34);(13,16)(17,19)(22,29)(25,33)(30,35)(32,34)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 17001);