Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#23717 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×#121 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
752 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)(16,19)(17,18)(20,21)(22,23,26,31,28,33,27,32)(24,29,35,44,36,45,42,49)(25,37,39,48,41,47,40,30)(34,46,38,52,50,53,51,43);(15,18)(19,21)(22,24)(23,29)(25,38)(26,35)(27,42)(28,36)(30,46)(31,44)(32,49)(33,45)(34,40)(37,52)(39,50)(41,51)(43,47)(48,53);(22,25,28,41)(23,30,33,48)(24,34,36,50)(26,40,27,39)(29,43,45,52)(31,47,32,37)(35,51,42,38)(44,53,49,46);(14,16,17,20)(15,19,18,21)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16705);