Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33853 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(19,24)(20,29)(21,30)(22,31)(25,36)(26,32)(27,42)(28,40)(34,35)(37,47)(38,39)(41,46)(43,49)(45,48);(18,19,23,27)(20,25,29,28)(21,32,34,48)(22,36,38,40)(24,39,42,31)(26,44,45,33)(30,41,35,49)(37,46,47,43);(15,17)(18,20,23,29)(19,25,27,28)(21,30,34,35)(22,31,38,39)(24,40,42,36)(26,43,45,46)(32,41,48,49)(33,47,44,37);(18,21,23,34)(19,26,27,45)(20,30,29,35)(22,37,38,47)(24,41,42,49)(25,43,28,46)(31,33,39,44)(32,40,48,36)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26841);