Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17518 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C42 | C24×C17 |
| socle | C22×C17 | C22×C22⋊C4 |
| prime radical | C17×#3482 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C4×#41×C17 ◁ G | |
1020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
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)(18,19,22,25,23,20,21,24)(26,27,32,29)(28,35,38,41)(30,34,31,39)(33,40,36,37);(18,20)(19,23)(21,25)(22,24)(26,28)(27,33)(29,36)(30,37)(31,40)(32,38)(34,41)(35,39);(18,21,23,22)(19,24,20,25)(26,29,32,27)(28,36,38,33)(30,34,31,39)(35,37,41,40);(18,21,23,22)(19,24,20,25)(26,30,32,31)(27,34,29,39)(28,37,38,40)(33,41,36,35)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10506);