Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#7916 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G | |
622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23)(24,30,32,27)(25,28)(26,29)(31,36,37,34)(33,35)(38,39,41,45,42,44,50,52)(40,46,48,53,47,43,49,51);(18,19,20,21)(22,24)(23,27)(25,31)(26,32)(28,34)(29,30)(33,37)(35,36)(38,40)(39,43)(41,49)(42,47)(44,46)(45,53)(48,50)(51,52);(22,25,26,33)(23,28,29,35)(24,31,32,37)(27,34,30,36)(40,47)(43,46)(48,49)(51,53)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 904);