Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C4×C13×#554 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
2516 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2,3,4)(21,22,23,24,25,26,27,28,29,30,31,32,33);(5,6,9,8)(7,11,12,10)(13,14,17,16)(15,19,20,18);(6,8)(10,11)(13,15,17,20)(14,18,16,19);(5,7)(6,10)(8,11)(9,12);(5,8,9,6)(7,11,12,10)(13,16,17,14)(15,18,20,19)1300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27155);