Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#7179 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C13 | D8 |
| commutator | C8 | C4×C8×C13 |
| Frattini, cosocle | C2×C4×C8 | C22×C13 |
| socle | C22×C13 | D4⋊C8 |
| prime radical | C23×C13 | #104 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C13 ◁ C22×C8×C13 ◁ C2×C4×C8×C13 ◁ G | |
274 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,21,27,23,28,30,26,24,29,20,25,22,32,31,33);(15,17)(19,25,28,33,29,27,32,26)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 167);