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×#62886 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6918 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,18)(19,21)(23,28)(24,32)(26,39)(30,36)(34,44)(37,50)(42,47)(51,53);(15,18)(19,20)(22,23,27,28)(24,29,32,33)(25,36,38,30)(26,31,39,40)(34,46,44,41)(35,42,45,47)(37,49,50,43)(48,53,52,51);(14,15)(16,19)(17,18)(20,21)(22,23)(24,33)(25,30)(26,31)(27,28)(29,32)(34,46)(35,47)(36,38)(37,43)(39,40)(41,44)(42,45)(48,53)(49,50)(51,52);(14,16)(15,19)(17,21)(18,20)(22,24)(23,29)(25,34)(26,35)(27,32)(28,33)(30,41)(31,42)(36,46)(37,48)(38,44)(39,45)(40,47)(43,51)(49,53)(50,52);(22,25,27,38)(23,30,28,36)(24,34,32,44)(26,37,39,50)(29,41,33,46)(31,43,40,49)(35,48,45,52)(42,51,47,53);(22,26)(23,31)(24,35)(25,37)(27,39)(28,40)(29,42)(30,43)(32,45)(33,47)(34,48)(36,49)(38,50)(41,51)(44,52)(46,53)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55874);