Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C2×C7×#2070 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2)(35,36,37,38,39,40,41);(3,4,7,21,8,12,23,11)(5,13,15,9,16,29,33,25)(6,17,19,26,20,10,22,27)(14,30,31,24,18,28,32,34);(3,5,7,15,8,16,23,33)(4,9,11,13,12,25,21,29)(6,18,19,32,20,14,22,31)(10,24,26,30,17,34,27,28);(3,6,8,20)(4,10,12,17)(5,14,16,18)(7,22,23,19)(9,24,25,34)(11,27,21,26)(13,28,29,30)(15,32,33,31)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16609);