Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C25 |
| direct product | C2×C8×C13×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | D4 |
| commutator | C4 | C23×C8×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle, prime radical | C23×C13 | C4×D4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ C2×C4×C8×C13 ◁ G | |
734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4,5,6,7,8,9,10);(11,12,13,14,15,16,17,18)(19,26,25,24,23,22,21,20);(11,19,15,23)(12,20,16,24)(13,21,17,25)(14,22,18,26)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10832);