Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3585 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#60182 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C23×D4 |
| commutator | C4 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C2×C17 | C22×C4×D4 |
| prime radical | C2×C17×#575 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×M16×C17 ◁ G | |
2628 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,28,24,27,22,36)(20,29,31,25,32,40,37,39)(21,26,35,42,33,41,34,46)(30,43,45,38,44,49,47,48);(18,20)(19,25)(21,30)(22,37)(23,31)(24,32)(26,38)(27,39)(28,40)(29,36)(33,44)(34,47)(35,45)(41,48)(42,49)(43,46);(18,21,23,35,24,33,22,34)(19,26,28,42,27,41,36,46)(20,30,31,45,32,44,37,47)(25,38,40,49,39,48,29,43);(21,33)(26,41)(30,44)(34,35)(38,48)(42,46)(43,49)(45,47);(19,27)(25,39)(26,41)(28,36)(29,40)(38,48)(42,46)(43,49)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53170);