Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3341 | 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)(22,23,28,31)(24,29,27,43)(25,35,38,52)(26,39,42,51)(30,45,47,37)(32,34,48,41)(33,50,36,49)(40,44,53,46);(14,16)(15,18)(17,21)(19,20)(22,24,28,27)(23,29,31,43)(25,36,38,33)(26,34,42,41)(30,46,47,44)(32,39,48,51)(35,49,52,50)(37,53,45,40);(22,25,28,38)(23,30,31,47)(24,33,27,36)(26,40,42,53)(29,44,43,46)(32,49,48,50)(34,45,41,37)(35,51,52,39);(16,21)(18,20)(23,31)(29,43)(30,47)(32,48)(35,52)(39,51)(44,46)(49,50)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26884);