Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#34193 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(23,25)(27,28)(31,34)(35,37);(22,23,26,25)(24,28,29,27);(22,23,26,25)(24,27,29,28)(30,31)(32,35)(33,34)(36,37);(22,24,26,29)(23,27,25,28);(22,25,26,23)(24,28,29,27)(30,32,33,36)(31,35,34,37)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27181);