Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C23×C42 |
| direct product | C13×#13822 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C13 | C24 |
| commutator | C22 | C22×C42×C13 |
| Frattini, cosocle | C24 | C24×C13 |
| prime radical | C25×C13 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1906 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19,21,20)(22,23,24,25)(26,27,30,29)(28,32,33,31);(18,19,21,20)(27,29)(31,32);(14,15,17,16)(18,19,21,20)(22,23)(24,25)(26,28)(27,31)(29,32)(30,33);(14,16,17,15)(18,20,21,19)(26,29,30,27)(28,32,33,31)1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6810);