Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C29 |
| direct product | C23×C17×Q32 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C17 | D8 |
| commutator, Frattini, cosocle | C8 | C25×C17 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
2078 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 5 generators on 55 points:
(1,2)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55);(3,4);(5,6);(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)(23,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24);(7,23,15,31)(8,24,16,32)(9,25,17,33)(10,26,18,34)(11,27,19,35)(12,28,20,36)(13,29,21,37)(14,30,22,38)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55615);