Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#12011 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | C2×D8 |
| commutator | C8 | C22×C8×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C2×C17 | C2×#335 |
| prime radical | C23×C17 | #108 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
220 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)(18,19,22,27,23,29,21,37,24,30,32,26,38,28,39,44)(20,31,35,42,36,46,34,25,33,41,47,43,49,45,48,40);(18,20,32,47,23,36,39,48,24,33,22,35,38,49,21,34)(19,25,37,45,28,42,27,41,30,40,44,46,29,43,26,31);(20,33)(25,40)(31,41)(34,48)(35,47)(36,49)(42,43)(45,46)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4999);