Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#12980 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C2×D4 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C8×D4 |
| prime radical | C2×C17×#135 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C22×C16×C17 ◁ G | |
470 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)(19,21)(22,23,27,33,28,34,47,38,29,35,48,52,26,32,37,50)(24,36,31,51,39,25,41,43,40,42,45,53,44,30,49,46);(18,19,20,21)(22,24,37,41,26,44,48,31,29,40,47,49,28,39,27,45)(23,30,50,51,32,42,52,46,35,25,38,53,34,36,33,43);(22,25)(23,31)(24,38)(26,36)(27,46)(28,42)(29,30)(32,49)(33,44)(34,41)(35,45)(37,53)(39,52)(40,50)(43,48)(47,51)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5968);