Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#18633 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
918 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)(18,19,23,27)(20,28,31,32)(21,26,22,25)(24,29,33,30)(34,35,38,41)(36,42,43,49)(37,45,46,40)(39,47,48,44);(18,20,23,31)(19,24,27,33)(21,30,22,29)(25,28,26,32)(37,46)(40,45)(42,49)(44,47);(34,36)(35,39)(37,47)(38,43)(40,49)(41,48)(42,45)(44,46);(18,21,23,22)(19,25,27,26)(20,29,31,30)(24,32,33,28)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11621);