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×#33846 |
| 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 | |
718 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
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)(18,19,23,27)(20,28,32,46)(21,33,36,49)(22,37,35,25)(24,39,41,30)(26,43,45,34)(29,42,47,40)(31,48,38,44);(18,20)(19,24)(21,29)(22,38)(23,32)(25,42)(26,44)(27,41)(28,33)(30,34)(31,35)(36,47)(37,40)(39,43)(45,48)(46,49);(15,17);(19,25)(20,29)(21,34)(22,35)(24,28)(26,45)(27,37)(30,31)(32,47)(36,43)(38,39)(40,48)(41,46)(42,44)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26834);