Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#7908 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C23×C13 | C2×C22⋊C4 |
| prime radical | C24×C13 | C22×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C22×C42×C13 ◁ G | |
802 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,20,23,21,22,24,25)(26,27,29,32,30,33,28,31);(14,15,16,17)(19,22)(20,24);(26,28,30,29)(27,31,33,32)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 896);