Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#12053 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C2×D4 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle, prime radical | C22×C17 | C8×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C4×C16×C17 ◁ G | |
206 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4352 |
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)(18,19,22,25)(20,26,28,33)(21,29,31,24)(23,30,32,27)(34,35,37,41,38,36,43,44,39,42,46,49,47,45,40,48);(18,20,22,28)(19,23,25,32)(21,30,31,27)(24,33,29,26);(34,36,37,44,38,42,43,49,39,45,46,48,47,35,40,41)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5041);