Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36755 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
1512 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)(20,24)(23,25)(26,27,29,31)(28,32,33,30)(34,35,38,39)(36,42,44,40)(37,41,45,46)(43,48,49,47);(19,22)(23,25)(35,39)(40,42)(41,46)(47,48);(18,19)(20,23)(21,22)(24,25)(26,28,29,33)(27,30,31,32)(34,35)(36,40)(37,41)(38,39)(42,44)(43,47)(45,46)(48,49);(18,19)(20,23)(21,22)(24,25)(34,36)(35,40)(37,43)(38,44)(39,42)(41,47)(45,49)(46,48);(18,20)(19,23)(21,24)(22,25)(34,37,38,45)(35,41,39,46)(36,43,44,49)(40,47,42,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29743);