Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11284 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #397 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1442 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
576 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)(18,19,23,27,24,28,22,37)(20,29,31,25,32,41,38,40)(21,33,36,48,35,26,34,42)(30,44,45,47,46,43,49,39);(18,20)(19,25)(21,30,35,46)(22,38)(23,31)(24,32)(26,39,33,47)(27,41)(28,40)(29,37)(34,49,36,45)(42,44,48,43);(18,21,22,34,24,35,23,36)(19,26,27,42,28,33,37,48)(20,30,31,45,32,46,38,49)(25,39,29,43,40,47,41,44)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4272);