Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C2×C17×#2950 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator | C4 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C17×#117 ◁ G | |
2654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2176 |
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);(3,4,6,5)(7,8)(9,17)(10,14)(11,23)(12,15)(13,19)(16,25)(18,31)(20,30)(21,29)(22,35)(24,27)(26,33)(28,34)(32,38)(36,37);(7,9,12,20)(8,13,15,27)(10,18,21,32)(11,24,25,19)(14,26,29,37)(16,30,23,17)(22,36,34,33)(28,38,35,31);(3,5,6,4)(7,10,12,21)(8,14,15,29)(9,18,20,32)(11,22,25,34)(13,26,27,37)(16,28,23,35)(17,31,30,38)(19,33,24,36);(8,15)(10,21)(13,27)(16,23)(17,30)(18,32)(22,34)(33,36)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53152);