Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#21427 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C2×C17×#121 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
1074 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27,30,34,31,33,38,28)(29,32,37,40,36,39,41,35);(26,28,30,33,31,34,38,27)(29,35,37,39,36,40,41,32);(19,22)(23,25)(26,29)(27,32)(28,35)(30,37)(31,36)(33,39)(34,40)(38,41);(18,20,21,24)(19,23,22,25)(29,36)(32,39)(35,40)(37,41)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14415);