Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11307 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #397 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1443 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
548 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)(20,24,29,38)(21,31)(22,35)(23,26)(25,33)(27,36)(28,37,42,49)(30,44,43,39)(32,45,47,40)(34,41)(46,48);(18,20)(19,24,26,38)(21,32,33,47)(22,30)(23,29)(25,40)(27,39,35,44)(28,34,42,48)(31,45)(36,43)(37,46)(41,49);(18,21)(19,25,26,31)(20,28,29,42)(22,34)(23,33)(24,37)(27,41,35,46)(30,32,43,47)(36,48)(38,49)(39,40)(44,45)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4295);