Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12825 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #476 |
| 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)(18,19,22,30,25,31,24,28)(20,32,34,26,35,29,23,40)(21,36,38,47,39,49,37,45)(27,42,43,33,44,41,46,48);(18,20,22,34,25,35,24,23)(19,26,28,32,31,40,30,29)(21,33,37,42,39,48,38,41)(27,36,43,47,44,49,46,45);(18,21)(19,27)(20,33)(22,37)(23,41)(24,38)(25,39)(26,36)(28,43)(29,45)(30,46)(31,44)(32,47)(34,42)(35,48)(40,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5813);