Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | Q16×#41×C17 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C23×D4 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C4×#41×C17 ◁ G | |
1826 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16);(17,18)(19,22)(20,21)(23,24);(18,21)(22,24);(17,19,20,23)(18,22,21,24)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54417);