Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C24×C17 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
1898 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 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)(23,27)(24,30)(29,34)(31,36)(38,39)(40,47)(41,44)(42,50)(43,46)(45,51)(48,52)(49,53);(23,27)(28,33)(29,34)(35,37)(38,40,43,41)(39,44,46,47)(42,48,51,49)(45,52,50,53);(22,23)(24,28)(25,29)(26,27)(30,33)(31,35)(32,34)(36,37)(38,41,43,40)(39,44,46,47)(42,49,51,48)(45,52,50,53);(22,24,26,30)(23,28,27,33)(25,31,32,36)(29,35,34,37)(38,39)(40,47)(41,44)(42,45)(43,46)(48,53)(49,52)(50,51);(22,25,26,32)(23,29,27,34)(24,31,30,36)(28,35,33,37)(38,42,43,51)(39,45,46,50)(40,48,41,49)(44,52,47,53)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27391);