Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#17993 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×C4×D4 |
| prime radical | C17×#466 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C17×#431 ◁ G | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
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)(18,19,24,29)(20,30,21,26)(22,28,23,27)(25,32,33,31)(34,35,38,42,39,41,47,48)(36,40,44,37,43,45,49,46);(18,20,24,21)(19,25,29,33)(22,31,23,32)(26,27,30,28)(34,36)(35,40)(37,42)(38,44)(39,43)(41,45)(46,48)(47,49);(18,21,24,20)(19,26,29,30)(22,31,23,32)(25,27,33,28)(34,37,38,45,39,46,47,40)(35,36,42,44,41,43,48,49);(18,22,24,23)(19,27,29,28)(20,31,21,32)(25,30,33,26)(35,41)(36,43)(42,48)(44,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10981);