Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23848 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#24998 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C22×D4×C17 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C4×Q8×C17 ◁ G | |
678 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)(18,19,21,22)(20,24,25,23)(26,27)(28,30)(29,31)(32,33)(34,35,37,40)(36,42,44,39)(38,41,46,49)(43,48,45,47);(19,22)(23,24)(26,28,29,32)(27,30,31,33)(34,36)(35,39)(37,44)(38,43)(40,42)(41,47)(45,46)(48,49);(27,31)(30,33)(36,43)(38,46)(39,47)(41,49)(42,48)(44,45);(18,20,21,25)(19,23,22,24)(35,40)(39,42)(41,49)(47,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 17986);