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×#60391 |
| 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 | |
4666 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)(14,15,20,17)(16,24,28,37)(18,22,31,29)(19,30,34,23)(21,33,25,27)(26,38,40,45)(32,42,43,36)(35,44,39,41);(14,16)(15,21)(17,25)(18,26)(19,33)(20,28)(22,35)(23,37)(24,30)(27,34)(29,39)(31,40)(32,44)(36,45)(38,42)(41,43);(14,17,20,15)(16,25,28,21)(18,29,31,22)(19,23,34,30)(24,33,37,27)(26,39,40,35)(32,36,43,42)(38,44,45,41);(14,18)(15,22)(16,26)(17,29)(19,32)(20,31)(21,35)(23,36)(24,38)(25,39)(27,41)(28,40)(30,42)(33,44)(34,43)(37,45);(18,31)(22,29)(26,40)(32,43)(35,39)(36,42)(38,45)(41,44)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 53379);