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×#18661 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C17×#3515 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
874 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)(18,19,22,24)(20,26,27,33)(21,29,31,25)(23,30,32,28)(34,35)(36,43)(37,41)(38,46)(39,42)(40,44)(45,48)(47,49);(18,20,22,27)(19,23,24,32)(21,30,31,28)(25,33,29,26)(34,35)(36,40)(37,41)(38,46)(39,42)(43,47)(44,48)(45,49);(34,36)(35,40)(37,44)(38,47)(39,45)(41,48)(42,49)(43,46);(19,24)(20,27)(25,29)(28,30)(34,37,39,38)(35,41,42,46)(36,44,45,47)(40,48,49,43)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11649);