Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13172 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #466 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | #135 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
274 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(18,19,21,20)(23,29)(24,33)(25,27)(26,39)(30,43)(31,47)(32,38)(34,40)(35,49)(36,48)(37,50)(41,45)(46,53)(51,52);(18,20,21,19)(22,23)(24,30)(25,38)(26,31)(27,29)(28,32)(33,45)(34,44)(35,51)(36,41)(37,46)(39,42)(40,47)(43,49)(48,53)(50,52);(22,24,34,48,27,36,26,33,28,37,39,49,25,35,40,50)(23,30,44,53,29,41,31,45,32,46,42,43,38,51,47,52)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6160);