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×#21837 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C24×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C22×C42×C17 ◁ G | |
1030 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(24,30)(25,28)(26,29)(27,32)(31,36)(33,35)(34,37)(38,39)(40,48)(41,47)(42,44)(43,46)(45,50)(49,53)(51,52);(22,24,26,32)(23,27,29,30)(25,33,34,31)(28,36,37,35)(39,44)(40,49)(46,47)(50,51);(22,25,26,34)(23,28,29,37)(24,31,32,33)(27,35,30,36)(38,40,42,49)(39,45,44,52)(41,50,43,51)(46,48,47,53);(23,29)(27,30)(28,37)(35,36)(38,41,42,43)(39,46,44,47)(40,50,49,51)(45,48,52,53)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14825);