Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11177 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #124 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #397 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
818 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)(22,23,27,33,28,31,26,32)(24,34,36,46,38,29,37,45)(25,39,41,48,43,49,42,30)(35,51,52,50,53,47,40,44);(18,19)(20,21)(22,24)(23,29)(25,40)(26,36)(27,37)(28,38)(30,47)(31,34)(32,45)(33,46)(35,42)(39,50)(41,53)(43,52)(44,49)(48,51);(19,21)(22,25)(23,30,31,48)(24,35)(26,41)(27,42)(28,43)(29,44,34,50)(32,39,33,49)(36,40)(37,52)(38,53)(45,47,46,51)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4165);