Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#7456 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #106 |
| commutator | C8 | C2×C16×C17 |
| Frattini, cosocle | C4×C16 | C22×C17 |
| socle | C2×C17 | #1367 |
| prime radical | C22×C17 | #364 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C2×C16×C17 ◁ C4×C16×C17 ◁ G | |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 2 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,29,24,28,35,45,25,30,33,44,21,37,36,48,26,31,41,47,38,46,34,49,23,42,40,27,39,43,20,32);(18,20,21,33,23,34,24,22,26,36,39,40,25,35,38,41)(19,27,28,32,30,29,37,45,31,44,46,48,42,47,43,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 444);