Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24×C4 |
| direct product | C7×#25937 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C22×C7×D4 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C4×C7×Q8 ◁ G | |
1028 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)(9,11)(12,13,16,19)(14,18,15,17)(20,21,24,28)(22,31,32,27)(23,34,33,35)(25,30,26,29);(12,14,16,15)(13,17,19,18)(20,22,24,32)(21,27,28,31)(23,25,33,26)(29,35,30,34);(8,9,10,11)(12,14,16,15)(13,18,19,17)(20,23,26,22,24,33,25,32)(21,27,30,35,28,31,29,34);(12,15,16,14)(13,18,19,17)(21,28)(27,31)(29,30)(34,35)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18925);