Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#34629 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| socle | C23×C17 | C25 |
| prime radical | C24×C17 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
1558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27,29,31)(28,30,32,33)(34,35)(36,39)(37,44)(38,40)(41,45)(42,47)(43,49)(46,48);(19,22)(23,25)(26,28,29,32)(27,30,31,33)(34,36,38,42)(35,39,40,47)(37,43,45,48)(41,46,44,49);(27,31)(30,33)(35,40)(36,42)(41,44)(43,48);(34,37,38,45)(35,41,40,44)(36,43,42,48)(39,46,47,49);(18,20,21,24)(19,23,22,25)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27617);