Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#34328 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2036 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19,22,21)(20,24,25,23)(27,28)(30,38)(32,34)(36,41);(26,27,31,28)(29,34,37,32)(30,33,38,35)(36,40,41,39);(18,20,22,25)(19,23,21,24)(26,28,31,27)(29,34,37,32)(30,35,38,33)(36,40,41,39);(18,19,22,21)(20,23,25,24)(26,29)(27,32)(28,34)(30,36)(31,37)(33,39)(35,40)(38,41);(14,16,17,15)(18,21,22,19)(20,24,25,23)(26,30)(27,33)(28,35)(29,36)(31,38)(32,39)(34,40)(37,41)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27316);