Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#33428 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #117 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C2×C8 | C24×C17 |
| socle | C2×C17 | C2×#432 |
| prime radical | C2×#41×C17 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C17×#405 ◁ G | |
528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,27,22,28,34,45,23,26,35,41,36,42,48,49)(20,29,31,43,32,39,47,44,30,24,33,37,46,25,38,40);(18,20)(19,24)(21,33)(22,32)(23,30)(25,28)(26,29)(27,43)(31,35)(34,38)(36,46)(37,41)(39,42)(40,49)(44,45)(47,48);(18,20)(19,25,26,39)(21,33)(22,32)(23,30)(24,28,29,42)(27,44,41,40)(31,35)(34,38)(36,46)(37,49,43,45)(47,48);(20,30)(24,29)(25,39)(31,33)(32,46)(37,43)(38,47)(40,44)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26416);