Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18682 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18711 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
818 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,27)(21,25)(22,30)(23,26)(24,28)(29,32)(31,33)(34,35,40,45)(36,46,42,49)(37,48,41,47)(38,43,39,44);(18,19)(20,24)(21,25)(22,30)(23,26)(27,31)(28,32)(29,33)(34,36,40,42)(35,41,45,37)(38,47,39,48)(43,46,44,49);(18,20)(19,24)(21,28)(22,31)(23,29)(25,32)(26,33)(27,30)(34,37,40,41)(35,42,45,36)(38,46,39,49)(43,47,44,48);(18,21,23,22)(19,25,26,30)(20,28,29,31)(24,32,33,27)(34,38,40,39)(35,43,45,44)(36,47,42,48)(37,49,41,46)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11699);