Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#23953 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3493 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1166 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)(16,20)(17,19)(18,21)(22,23)(24,29)(25,36)(26,31)(27,40)(28,32)(30,38)(33,49)(34,43)(35,45)(37,47)(39,48)(41,44)(42,50)(46,52)(51,53);(14,16,17,21)(15,18,19,20)(22,24)(23,29)(25,33)(26,34)(27,41)(28,35)(30,46)(31,43)(32,45)(36,49)(37,50)(38,52)(39,51)(40,44)(42,47)(48,53);(22,25,28,39)(23,30,32,47)(24,33,35,51)(26,38,27,37)(29,42,45,46)(31,48,40,36)(34,52,41,50)(43,49,44,53);(15,19)(18,20)(22,26,28,27)(23,31,32,40)(24,34,35,41)(25,37,39,38)(29,43,45,44)(30,36,47,48)(33,50,51,52)(42,53,46,49)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16941);