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) = C24 |
| direct product | C13×#33870 |
| 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 | |
558 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19)(16,20,21,18)(22,23,28,32)(24,29,27,42)(25,35,37,51)(26,38,41,52)(30,45,47,36)(31,34,49,40)(33,50,43,48)(39,44,53,46);(14,16)(15,18)(17,21)(19,20)(22,24,28,27)(23,29,32,42)(25,33,37,43)(26,34,41,40)(30,44,47,46)(31,38,49,52)(35,50,51,48)(36,39,45,53);(22,25)(23,30)(24,33)(26,39)(27,43)(28,37)(29,44)(31,48)(32,47)(34,45)(35,38)(36,40)(41,53)(42,46)(49,50)(51,52);(16,21)(18,20)(22,24,28,27)(23,29,32,42)(25,33,37,43)(26,34,41,40)(30,44,47,46)(31,38,49,52)(35,50,51,48)(36,39,45,53)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26858);