Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#12982 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #120 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1869 |
| prime radical | C17×#532 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ G | |
474 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)(18,19,23,29,24,30,42,48,25,28,43,47,22,27,32,45)(20,31,35,40,33,46,49,21,34,37,41,36,39,26,44,38);(18,20,32,49,22,39,43,35,25,34,42,44,24,33,23,41)(19,26,45,40,27,37,47,38,28,46,48,36,30,31,29,21);(18,21)(19,20)(22,40)(23,31)(24,36)(25,38)(26,32)(27,39)(28,34)(29,41)(30,33)(35,47)(37,43)(42,46)(44,48)(45,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5970);