Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9415 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9415 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,27,28,31)(21,24,29,30)(22,25)(23,26)(32,33)(34,35)(36,39,43,48)(37,40)(38,41)(42,45)(44,46,49,47);(18,20,22,30,23,28,32,24)(19,21,25,31,26,29,33,27)(34,36)(35,39,41,48)(37,44)(38,43)(40,46,42,47)(45,49);(18,21)(19,24)(20,25)(22,31)(23,29)(26,30)(27,32)(28,33)(35,40)(37,45)(39,46)(41,42)(44,49)(47,48)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2403);