Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13329 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C22×C13×D8 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
578 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)(16,17)(22,23,27,32)(24,33,36,51)(25,29,40,47)(26,41,39,31)(28,43,45,34)(30,48,46,38)(35,52,42,49)(37,50,53,44);(15,17)(18,19)(20,21)(22,24,27,36)(23,28,32,45)(25,37,40,53)(26,42,39,35)(29,33,47,51)(30,49,46,52)(31,50,41,44)(34,48,43,38);(19,21)(23,29)(25,38)(26,39)(28,33)(30,31)(32,47)(34,37)(35,42)(40,48)(41,46)(43,53)(44,52)(45,51)(49,50)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6317);