Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C23×C13 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 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)(24,33)(25,39)(26,31)(27,44)(28,32)(29,35)(30,42)(34,49)(36,46)(37,53)(38,51)(40,48)(41,47)(43,50)(45,52);(14,16,17,21)(15,18,19,20)(22,23)(24,34)(25,30)(26,44)(27,31)(28,32)(29,36)(33,49)(35,46)(37,45)(38,48)(39,42)(40,51)(41,50)(43,47)(52,53);(22,24,28,38)(23,29,32,45)(25,40,43,49)(26,37,27,36)(30,46,47,53)(31,48,44,34)(33,50,51,39)(35,41,52,42)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6358);