Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12822 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #459 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1802 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C2×C4×C8×C17 ◁ G | |
400 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)(18,19,24,28,25,30,22,38)(20,29,23,39,33,46,32,26)(21,34,36,49,37,41,35,45)(27,40,42,48,44,47,43,31);(18,20,22,32,25,33,24,23)(19,26,28,29,30,39,38,46)(21,31,35,47,37,48,36,40)(27,41,42,45,44,34,43,49);(18,21)(19,27)(20,31)(22,35)(23,40)(24,36)(25,37)(26,41)(28,42)(29,45)(30,44)(32,47)(33,48)(34,39)(38,43)(46,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5810);