Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#36773 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C17×#2635 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
1574 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)(28,32)(30,33)(34,35)(36,40)(37,39)(38,45)(41,46)(42,44)(43,48)(47,49);(19,22)(23,25)(26,27,29,31)(28,30,32,33)(35,37)(40,42)(41,45)(47,48);(18,19)(20,23)(21,22)(24,25)(26,28,29,32)(27,30,31,33)(34,36,39,44)(35,40,37,42)(38,43,46,49)(41,47,45,48);(18,19)(20,23)(21,22)(24,25)(34,37,39,35)(36,42,44,40)(38,45,46,41)(43,48,49,47);(18,20)(19,23)(21,24)(22,25)(34,38,39,46)(35,41,37,45)(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, 29761);