Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9091 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#11015 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #386 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
1242 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)(22,23,27,33,28,31,26,32)(24,34,37,44,38,29,36,45)(25,30,40,48,41,47,42,49)(35,50,39,53,51,43,52,46);(22,24,28,38)(23,29,31,34)(25,39,41,52)(26,37,27,36)(30,46,47,53)(32,45,33,44)(35,42,51,40)(43,49,50,48);(19,21)(22,25)(23,30)(24,35)(26,42)(27,40)(28,41)(29,43)(31,47)(32,49)(33,48)(34,50)(36,52)(37,39)(38,51)(44,53)(45,46)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4003);