Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C17 · Schur multiplier (H2) = C2×C43 |
| direct product | C17×#13793 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C17 | C24 |
| commutator | C22 | C22×C42×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
1498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(22,23,25,24)(27,30)(31,33)(34,35)(36,38)(37,40)(39,41);(22,23,25,24)(35,36)(39,40);(26,27,29,30)(28,31,32,33)(34,36,38,35)(37,40,41,39);(18,20,21,19)(22,24,25,23)(26,28,29,32)(27,31,30,33)(34,37)(35,39)(36,40)(38,41)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6781);