Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×C16×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C13×C16 | C22 |
| commutator | C2 | C2×C4×C13×C16 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle, prime radical | C23×C13 | C22×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13×C16 ◁ G | |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29);(31,33)(34,35,36,37);(30,31,32,33)2080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5649);