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×#33851 |
| 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 | |
674 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)(20,28)(21,33)(22,36)(25,29)(26,45)(27,41)(31,32)(34,38)(35,47)(37,39)(40,46)(43,49)(44,48);(18,19,23,27)(20,29,32,48)(21,34,37,45)(22,38,36,26)(24,39,41,33)(25,42,44,30)(28,40,31,49)(35,46,47,43);(15,17);(18,20,23,32)(19,25,27,44)(21,35,37,47)(22,28,36,31)(24,40,41,49)(26,46,38,43)(29,45,48,34)(30,39,42,33)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26839);