Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#23674 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×#121 |
| prime radical | C24×C13 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
766 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
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)(16,21)(17,19)(18,20)(22,23,26,31,28,33,27,32)(24,29,35,44,36,45,42,49)(25,37,40,48,41,47,39,30)(34,46,38,52,51,53,50,43);(14,16,18,17)(15,19,20,21)(22,24)(23,29)(25,38)(26,35)(27,42)(28,36)(30,46)(31,44)(32,49)(33,45)(34,39)(37,52)(40,51)(41,50)(43,47)(48,53);(14,17,18,16)(15,19,20,21)(22,25)(23,30)(24,34)(26,39)(27,40)(28,41)(29,43)(31,47)(32,37)(33,48)(35,50)(36,51)(38,42)(44,53)(45,52)(46,49);(22,26,28,27)(23,31,33,32)(24,35,36,42)(25,39,41,40)(29,44,45,49)(30,47,48,37)(34,50,51,38)(43,53,52,46)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16662);