Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13×C16 · Schur multiplier (H2) = C23 |
| direct product | C13×#7167 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | D4 |
| commutator | C4 | C4×C13×C16 |
| Frattini, cosocle | C2×C4×C8 | C22×C13 |
| socle, prime radical | C23×C13 | C22⋊C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ C2×C4×C8×C13 ◁ G | |
286 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(19,23)(20,21)(24,25)(26,27,29,34,31,28,33,37,32,36,30,35,40,39,41,38);(15,17)(18,19,21,24,22,25,20,23)(26,28,30,38,31,36,41,34,32,39,29,37,40,27,33,35)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 155);