Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C13 · Schur multiplier (H2) = C2×C8 |
| direct product | C13×#8262 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C13 | C23 |
| commutator | C22 | C2×C4×C8×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle, prime radical | C23×C13 | C2×C42 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C13 ◁ G | |
494 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19,21,20,22,23,25,24);(15,17)(26,27,28,30,29,31,32,33);(18,20,21,23,22,24,25,19)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1250);