Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#60184 |
| 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 | C17×#3584 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×C17×#131 ◁ G | |
2604 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)(18,19,23,28,24,20,29,27)(21,30,33,39,34,25,37,40)(22,26,36,42,35,31,43,41)(32,44,46,48,45,38,47,49);(18,20)(19,24)(21,30)(22,31)(23,27)(25,34)(26,35)(28,29)(32,44)(33,39)(36,41)(37,40)(38,45)(42,43)(46,48)(47,49);(18,21,23,33,24,34,29,37)(19,25,28,40,20,30,27,39)(22,32,36,46,35,45,43,47)(26,38,42,49,31,44,41,48);(18,22)(19,26)(20,31)(21,32)(23,36)(24,35)(25,38)(27,41)(28,42)(29,43)(30,44)(33,46)(34,45)(37,47)(39,48)(40,49);(22,35)(26,31)(32,45)(36,43)(38,44)(41,42)(46,47)(48,49)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53172);