Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#12623 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #99 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| socle | C2×C17 | C4×#99 |
| prime radical | C17×#525 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C2×C8×C17 ◁ C2×C17×#131 ◁ G | |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,28,24,21,26,35)(20,29,32,46,33,43,40,49)(22,27,37,44,38,34,42,48)(25,39,41,36,30,45,47,31);(18,20)(19,25)(21,30)(22,36,38,31)(23,32)(24,33)(26,40)(27,43,34,29)(28,41)(35,47)(37,45,42,39)(44,49,48,46);(18,21,23,35,24,19,26,28)(20,30,32,47,33,25,40,41)(22,34,37,48,38,27,42,44)(29,45,46,31,43,39,49,36)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5611);