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) = C22 |
| direct product | C13×#7163 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C13 | D4 |
| commutator | C4 | C4×C13×C16 |
| Frattini, cosocle | C2×C4×C8 | C22×C13 |
| socle | C22×C13 | #336 |
| prime radical | C23×C13 | C4⋊C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C13 ◁ C2×C4×C8×C13 ◁ G | |
238 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 2 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,18)(17,20)(19,21)(22,23,25,30,27,24,29,33,28,32,26,31,36,35,37,34);(15,18,20,19)(22,24,26,34,27,32,37,30,28,35,25,33,36,23,29,31)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 151);