Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#20668 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C22×C4⋊C4 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×#41×C17 ◁ G | |
1322 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 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)(22,23,27,31,28,32,26,41)(24,33,36,43,37,47,35,29)(25,30,40,45,38,44,39,51)(34,46,50,52,48,53,49,42);(22,24,26,35,28,37,27,36)(23,29,31,33,32,43,41,47)(25,34,39,49,38,48,40,50)(30,42,45,46,44,52,51,53);(19,21)(22,25)(23,30)(24,34)(26,39)(27,40)(28,38)(29,42)(31,45)(32,44)(33,46)(35,49)(36,50)(37,48)(41,51)(43,52)(47,53);(25,38)(30,44)(34,48)(39,40)(42,52)(45,51)(46,53)(49,50)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13656);