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×#18643 |
| 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 | |
906 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)(34,35,39,43)(36,44,47,48)(37,40,38,42)(41,46,49,45);(18,20,23,31)(19,24,27,33)(21,30,22,29)(25,28,26,32)(35,40)(37,38)(41,48)(42,43)(44,49)(45,46);(34,36)(35,41)(37,45)(38,46)(39,47)(40,48)(42,44)(43,49);(18,21,23,22)(19,25,27,26)(20,29,31,30)(24,32,33,28)(34,37,39,38)(35,42,43,40)(36,45,47,46)(41,44,49,48)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11631);