Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13030 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13030 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1879 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C17×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19,22,27,23,29,39,43,24,30,21,28,38,47,36,25)(20,31,33,44,34,46,40,45,35,42,32,49,41,48,37,26);(19,25,30,43)(21,36)(22,39)(23,38)(26,42,45,31)(27,29,28,47)(32,37)(33,40)(34,41)(44,46,49,48);(18,20)(19,26)(21,37)(22,40)(23,41)(24,35)(25,42)(27,46)(28,48)(29,49)(30,45)(31,43)(32,36)(33,39)(34,38)(44,47)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6018);