Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#34372 |
| 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 | |
1910 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)(22,23,27,25)(24,28,32,30)(26,33,34,29)(31,36,37,35)(39,43)(40,46)(41,49)(51,53);(23,25)(28,30)(29,33)(35,36)(38,39,42,43)(40,47,46,44)(41,45,49,50)(48,53,52,51);(22,24,27,32)(23,28,25,30)(26,31,34,37)(29,35,33,36)(38,39)(40,44)(41,45)(42,43)(46,47)(48,51)(49,50)(52,53);(22,25,27,23)(24,30,32,28)(26,33,34,29)(31,36,37,35)(38,40,42,46)(39,44,43,47)(41,48,49,52)(45,51,50,53);(22,26)(23,29)(24,31)(25,33)(27,34)(28,35)(30,36)(32,37)(38,41)(39,45)(40,48)(42,49)(43,50)(44,51)(46,52)(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, 27360);