Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13162 |
| 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 | C23×C17 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C22×C16×C17 ◁ G | |
290 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)(22,23,27,33,28,32,43,49,29,34,42,31,26,44,25,40)(24,30,37,45,38,46,35,50,39,47,51,48,36,52,41,53);(19,21)(22,24,27,37,28,38,43,35,29,39,42,51,26,36,25,41)(23,30,33,45,32,46,49,50,34,47,31,48,44,52,40,53);(22,25,26,42,29,43,28,27)(23,31,32,40,34,33,44,49)(24,35,36,37,39,41,38,51)(30,45,46,50,47,48,52,53)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6150);