Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9345 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#9362 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,26,23,27,21,24)(20,28,30,25,31,32,29,33)(34,35)(36,39,43,46)(37,40)(38,41)(42,45,48,49)(44,47);(19,24,27,26)(25,28,33,32)(34,36)(35,39,41,46)(37,42)(38,43)(40,45,47,49)(44,48);(18,20,23,31)(19,25,27,33)(21,29,22,30)(24,28,26,32)(34,37,38,44)(35,40,41,47)(36,42,43,48)(39,45,46,49)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2350);