Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C2×C13×#3170 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| socle | C23×C13 | C22×D4 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ C22×C42×C13 ◁ G | |
2006 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 39 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4)(5,8)(6,7)(9,10)(11,12,15,18)(13,19,22,26)(14,23,20,17)(16,24,25,21);(4,7)(8,10);(11,13,20,24,15,22,14,21)(12,16,23,26,18,25,17,19);(3,5,6,9)(4,8,7,10)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53660);