Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#12563 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #106 |
| commutator | C8 | C2×C42×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×#106 |
| prime radical | C24×C17 | SD16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ C23×C8×C17 ◁ G | |
570 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,35,38,48)(25,31)(26,43)(27,44)(28,45)(29,34)(30,37,47,39)(32,42)(33,41)(36,49,40,53)(46,51,50,52);(19,21)(22,24,27,39,28,40,41,51,29,38,26,37,25,36,42,52)(23,30,33,48,31,46,44,53,34,47,32,35,45,50,43,49);(22,25,29,28)(23,31,34,45)(24,36,38,40)(26,41,27,42)(30,46,47,50)(32,43,33,44)(35,49,48,53)(37,51,39,52)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5551);