Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C42×C13×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C13 | D4 |
| commutator | C4 | C22×C42×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| socle, prime radical | C23×C13 | C22×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C13 ◁ C43×C13 ◁ G | |
1110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4)(25,26,27,28,29,30,31,32,33,34,35,36,37);(5,6,7,8);(9,10,11,12,13,14,15,16)(17,24,23,22,21,20,19,18);(9,17,13,21)(10,18,14,22)(11,19,15,23)(12,20,16,24)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13487);