Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62892 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62933 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6720 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 6 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,23)(18,22)(19,21)(20,25)(26,38)(27,31)(28,35)(29,34)(30,36)(32,39)(33,40)(37,42)(41,43)(44,45);(14,16,19,27)(15,20,21,33)(17,26,28,41)(18,25,29,40)(22,24,34,31)(23,32,35,44)(30,39,42,45)(36,38,37,43);(15,21)(16,25)(20,31)(22,34)(23,35)(24,33)(26,39)(27,40)(32,43)(36,37)(38,44)(41,45);(15,22)(17,28)(20,24)(21,34)(23,37)(26,41)(30,42)(31,33)(32,43)(35,36)(38,44)(39,45);(14,17,29,42)(15,23,34,37)(16,26,40,45)(18,30,19,28)(20,32,31,43)(21,35,22,36)(24,38,33,44)(25,39,27,41);(15,21)(20,33)(22,34)(23,35)(24,31)(32,44)(36,37)(38,43)949 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55921);