Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#10745 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #120 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C25 | C23×C17 |
| prime radical | C23×D4×C17 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C25×C17 ◁ G | |
1794 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(26,27)(28,32,33,30)(29,31);(22,23,24,25)(26,28)(27,30)(29,33)(31,32);(19,21)(26,27)(28,30)(29,31)(32,33)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3733);