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×#33869 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3283 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C4×D4×C13 ◁ C8×D4×C13 ◁ G | |
546 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)(24,29)(25,35)(26,38)(27,42)(28,32)(30,36)(31,40)(33,49)(34,48)(37,51)(39,44)(41,52)(43,47)(45,53)(46,50);(14,16)(15,18)(17,21)(19,20)(22,24,28,27)(23,29,32,42)(25,33,37,43)(26,34,41,40)(30,44,46,45)(31,38,48,52)(35,49,51,47)(36,39,50,53);(22,25)(23,30)(24,33)(26,39)(27,43)(28,37)(29,44)(31,47)(32,46)(34,50)(35,38)(36,40)(41,53)(42,45)(48,49)(51,52);(16,21)(18,20)(22,24,28,27)(23,29,32,42)(25,33,37,43)(26,34,41,40)(30,44,46,45)(31,38,48,52)(35,49,51,47)(36,39,50,53)715 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26857);