Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C29 |
| direct product | C2×C13×#2327 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C24 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
2958 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 3328 |
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);(4,6)(7,8,10,9)(12,16)(13,19)(14,22)(24,26);(7,9,10,8)(11,12)(13,20)(14,18)(15,16)(17,19)(21,26)(22,23)(24,25);(3,4,5,6)(11,13)(12,17)(14,21)(15,19)(16,20)(18,24)(22,25)(23,26);(11,14,15,22)(12,18,16,23)(13,21,19,25)(17,24,20,26)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27056);