Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13229 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#13234 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1964 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C17×#3058 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C17×#131 ◁ G | |
464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
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)(18,19,24,28,25,29,23,41)(20,22,27,39,33,40,32,30)(21,34,37,43,38,48,36,26)(31,45,42,49,47,44,46,35);(18,20,30,19)(21,31,44,26)(22,28,23,32)(24,27,40,41)(25,33,39,29)(34,36,46,35)(37,42,49,48)(38,47,45,43);(18,21,24,37,25,38,23,36)(19,26,41,48,29,43,28,34)(20,31,27,42,33,47,32,46)(22,35,30,44,40,49,39,45)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6222);