Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63041 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#63046 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6790 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)(14,15,19,23)(16,25,27,21)(17,28,31,38)(18,22,33,37)(20,24,34,29)(26,39,41,35)(30,40,43,45)(32,36,44,42);(14,16,19,27)(15,21,23,25)(17,29,31,24)(18,26,33,41)(20,28,34,38)(22,35,37,39)(30,42,43,36)(32,40,44,45);(14,17)(15,16)(18,30)(19,31)(20,21)(22,26)(23,27)(24,28)(25,34)(29,38)(32,35)(33,43)(36,40)(37,41)(39,44)(42,45);(14,15)(16,17)(18,22)(19,23)(20,24)(21,28)(25,38)(26,30)(27,31)(29,34)(32,36)(33,37)(35,40)(39,45)(41,43)(42,44);(14,18,19,33)(15,22,23,37)(16,26,27,41)(17,30,31,43)(20,32,34,44)(21,35,25,39)(24,36,29,42)(28,40,38,45);(18,32)(22,36)(26,40)(30,35)(33,44)(37,42)(39,43)(41,45)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56034);