Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13027 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #459 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1879 |
| prime radical | C17×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
484 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)(18,19,23,28,24,30,41,48,25,31,21,38,40,43,22,29)(20,32,35,45,36,44,34,46,37,49,33,27,42,47,39,26);(18,20)(19,26,31,46)(21,39)(22,33)(23,34)(24,42)(25,37)(27,43,45,30)(28,44,38,47)(29,49,48,32)(35,41)(36,40);(18,20)(19,27)(21,39)(22,33)(23,34)(24,42)(25,37)(26,43)(28,32)(29,44)(30,46)(31,45)(35,41)(36,40)(38,49)(47,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6015);