Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C29 |
| direct product | C17×#60183 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | C22×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 ◁ C8×C17 ◁ C2×C17×#131 ◁ G | |
2612 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)(21,25,33,39,34,30,42,38)(22,26,36,41,35,31,43,40)(32,37,46,48,45,44,49,47);(18,20)(19,24)(21,30)(22,31)(23,27)(25,34)(26,35)(28,29)(32,44)(33,38)(36,40)(37,45)(39,42)(41,43)(46,47)(48,49);(18,21,23,33,24,34,29,42)(19,25,28,39,20,30,27,38)(22,32,36,46,35,45,43,49)(26,37,41,48,31,44,40,47);(18,22)(19,26)(20,31)(21,32)(23,36)(24,35)(25,37)(27,40)(28,41)(29,43)(30,44)(33,46)(34,45)(38,47)(39,48)(42,49);(22,35)(26,31)(32,45)(36,43)(37,44)(40,41)(46,49)(47,48)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53171);