Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23860 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C7×#23983 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×D4 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×D4 ◁ G | |
1228 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)(8,9)(10,11)(12,13)(14,18)(15,17)(16,19)(20,21,26,22)(23,31,34,35)(24,28,25,29)(27,33,30,32);(12,14,15,19)(13,16,17,18)(20,22,26,21)(23,31,34,35)(24,29,25,28)(27,33,30,32);(9,11)(20,23,26,34)(21,27,22,30)(24,33,25,32)(28,31,29,35);(13,17)(16,18)(20,24,26,25)(21,28,22,29)(23,32,34,33)(27,35,30,31)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16971);