Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#21075 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #121 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C22×C17 | C2×#121 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
1014 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)(18,19,21,20)(22,23)(24,33)(25,38)(26,31)(27,42)(28,32)(29,36)(30,41)(34,48)(35,44)(37,47)(39,53)(40,45)(43,49)(46,51)(50,52);(18,20,21,19)(22,24,27,36,28,37,26,35)(23,29,31,33,32,44,42,47)(25,34,40,50,41,51,39,49)(30,43,45,46,38,52,53,48);(22,25,27,40,28,41,26,39)(23,30,31,45,32,38,42,53)(24,34,36,50,37,51,35,49)(29,43,33,46,44,52,47,48);(22,26,28,27)(23,31,32,42)(24,35,37,36)(25,39,41,40)(29,33,44,47)(30,45,38,53)(34,49,51,50)(43,46,52,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14063);