Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#11273 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #394 |
| 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)(20,24,29,39)(21,31)(22,35)(23,26)(25,33)(27,36)(28,42,32,47)(30,46,45,38)(34,48)(37,49,40,44)(41,43);(18,20,22,30,23,29,36,45)(19,24,27,38,26,39,35,46)(21,32,33,49,34,28,43,44)(25,40,31,47,41,37,48,42);(18,21)(19,25,26,41)(20,28,29,32)(22,33)(23,34)(24,37)(27,31,35,48)(30,44,45,49)(36,43)(38,42)(39,40)(46,47)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4261);