Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60388 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C210 |
| direct product | C13×#60390 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C22×#120 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C13×#41 ◁ G | |
4698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(18,29)(21,34)(22,33)(23,30)(25,31)(28,40)(32,36)(35,44)(37,41)(39,42)(43,45);(14,15)(16,21)(17,22)(18,30)(19,23)(20,29)(24,35)(25,32)(26,36)(27,37)(28,41)(31,34)(33,40)(38,45)(39,43)(42,44);(14,16,19,26)(15,21,23,36)(17,24,27,38)(18,31,29,25)(20,32,30,34)(22,35,37,45)(28,42,40,39)(33,43,41,44);(14,17)(15,22)(16,24)(18,28)(19,27)(20,33)(21,35)(23,37)(25,39)(26,38)(29,40)(30,41)(31,42)(32,43)(34,44)(36,45);(17,27)(22,37)(24,38)(28,40)(33,41)(35,45)(39,42)(43,44)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53378);