Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19621 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#19634 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C23×C17 | #127 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
698 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)(20,26)(21,29)(22,24)(23,28)(25,30)(27,32)(31,33)(34,35,38,41)(36,42,45,49)(37,46,43,40)(39,47,48,44);(18,20,21,28,22,27,30,33)(19,23,25,26,24,31,29,32);(19,24)(23,31)(25,29)(26,32)(34,36,43,47,38,45,37,44)(35,39,46,49,41,48,40,42);(20,27)(23,31)(26,32)(28,33)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12622);