Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#19620 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #127 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C2×#127 |
| prime radical | C17×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
712 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)(18,19,22,25)(20,26,27,33)(21,29,30,24)(23,31,32,28)(34,35)(36,43)(37,41)(38,47)(39,42)(40,45)(44,48)(46,49);(18,20,21,28,22,27,30,31)(19,23,24,26,25,32,29,33);(20,27)(23,32)(26,33)(28,31)(34,36,38,45,39,46,37,44)(35,40,41,43,42,48,47,49);(34,37,39,38)(35,41,42,47)(36,44,46,45)(40,43,48,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12608);