Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C2×C13×#3509 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
7022 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 6 generators on 39 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39);(5,9)(7,10)(11,12,15,18)(13,16,21,19)(14,22,23,17)(20,25,26,24);(3,4,6,8)(5,7,9,10)(11,12)(13,19)(14,17)(15,18)(16,21)(20,25)(22,23)(24,26);(3,5,6,9)(4,7,8,10);(11,13)(12,16)(14,20)(15,21)(17,24)(18,19)(22,25)(23,26);(11,14,15,23)(12,17,18,22)(13,20,21,26)(16,24,19,25)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55792);