Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17517 |
| 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×#3481 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C4×#41×C17 ◁ G | |
1096 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)(18,19,21,24,22,20,25,23)(26,27)(28,32)(29,31)(30,34)(33,37)(35,39)(36,38)(40,41);(18,20)(19,22)(21,23)(24,25)(27,31)(29,37)(32,38)(33,34)(36,41)(39,40);(26,28)(27,32)(29,36)(30,35)(31,38)(33,40)(34,39)(37,41);(28,35)(32,39)(36,41)(38,40)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10505);