Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#20884 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C8×C17 ◁ G | |
1342 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)(22,23,27,32,28,31,26,40)(24,33,35,29,36,45,41,44)(25,37,38,30,39,47,42,46)(34,43,50,53,51,52,49,48);(19,21)(22,24,27,35,28,36,26,41)(23,29,32,45,31,44,40,33)(25,34,38,50,39,51,42,49)(30,43,47,53,46,52,37,48);(22,25)(23,30)(24,34)(26,42)(27,38)(28,39)(29,43)(31,46)(32,47)(33,48)(35,50)(36,51)(37,40)(41,49)(44,52)(45,53);(23,31)(29,44)(30,46)(32,40)(33,45)(37,47)(43,52)(48,53)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13872);