Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11208 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C17 | C2×D4 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ C22×C42×C17 ◁ G | |
870 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(26,27,28,29)(30,31)(32,35)(33,36)(34,37);(18,19,21,20)(22,23)(24,25)(30,32,34,33)(31,35,37,36);(18,20,21,19)(23,25)(31,36)(32,33)(35,37)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4196);