Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| prime radical | C13×#3455 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6186 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,21)(16,22,24,17)(18,26,27,20)(23,25,29,28)(30,31,35,36)(32,40,43,37)(33,38,44,48)(34,46,47,39)(41,52,54,49)(42,50,56,53)(45,58,57,51)(55,59,61,60);(14,16,19,24)(15,17,21,22)(18,23,27,29)(20,25,26,28)(31,36)(33,44)(37,40)(39,46)(41,54)(45,57)(50,53)(55,61);(14,17)(15,16)(18,25)(19,22)(20,23)(21,24)(26,29)(27,28)(30,31)(32,40)(33,38)(34,39)(35,36)(37,43)(41,52)(42,53)(44,48)(45,51)(46,47)(49,54)(50,56)(55,60)(57,58)(59,61);(14,18,19,27)(15,20,21,26)(16,23,24,29)(17,25,22,28)(30,32,35,43)(31,37,36,40)(33,41,44,54)(34,42,47,56)(38,49,48,52)(39,50,46,53)(45,55,57,61)(51,59,58,60);(30,33,35,44)(31,38,36,48)(32,41,43,54)(34,45,47,57)(37,49,40,52)(39,51,46,58)(42,55,56,61)(50,59,53,60);(30,34)(31,39)(32,42)(33,45)(35,47)(36,46)(37,50)(38,51)(40,53)(41,55)(43,56)(44,57)(48,58)(49,59)(52,60)(54,61)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55877);