Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13175 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13175 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1943 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | #137 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
256 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)(19,25)(20,29,32,45)(21,23)(22,36)(26,40,42,43)(27,37)(28,34)(30,41,47,49)(31,46,33,44)(35,38);(18,19)(20,30,32,47)(21,34)(22,37)(23,25)(24,28)(26,33,42,31)(27,38)(29,43,45,40)(35,39)(36,48)(41,44,49,46);(18,20,22,29,23,33,36,46,24,32,38,45,21,31,35,44)(19,26,27,41,25,30,39,40,28,42,37,49,34,47,48,43)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6163);