Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12963 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | B(4,𝔽2) |
| commutator | C2×D4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| socle | C2×C17 | #1867 |
| prime radical | C17×#525 | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C4×C17 ◁ C2×#41×C17 ◁ G | |
416 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)(18,19,22,26,23,27,34,40)(20,28,31,42,29,41,44,49)(21,25,33,39,32,38,45,48)(24,35,37,43,36,46,47,30);(18,20,22,31,23,29,34,44)(19,24,26,37,27,36,40,47)(21,30,33,35,32,43,45,46)(25,28,39,42,38,41,48,49);(20,29)(21,32)(24,36)(28,41)(31,44)(33,45)(37,47)(42,49)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5951);