Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C13 · Schur multiplier (H2) = C27 |
| direct product | C22×C13×#324 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C13 | C22⋊C4 |
| commutator | C22 | C23×C8×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C25×C13 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ C24×C4×C13 ◁ G | |
1806 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2)(21,22,23,24,25,26,27,28,29,30,31,32,33);(3,4);(5,6)(7,11,12,9)(8,10)(13,14,15,17,16,18,19,20);(5,7,8,12)(6,9,10,11)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10332);