Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#7927 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | C2×#95 |
| prime radical | C25×C17 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C24×C4×C17 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24,25,22)(21,23)(26,27,29,34,31,33,30,35)(28,32,36,40,38,39,37,41);(18,20)(19,22)(21,25)(23,24)(26,28,30,37,31,38,29,36)(27,32,35,41,33,39,34,40);(27,33)(32,39)(34,35)(40,41)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 915);