Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#62860 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| prime radical | C13×#3449 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6866 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)(15,18)(19,21)(23,24)(27,40)(29,32)(30,33)(36,49)(38,50)(41,44)(47,53);(14,15)(16,19)(17,18)(20,21)(22,23,28,24)(25,29,37,32)(26,33,39,30)(27,31,40,34)(35,44,48,41)(36,42,49,45)(38,46,50,43)(47,52,53,51);(14,16,17,20)(15,19,18,21)(22,24,28,23)(25,29,37,32)(26,33,39,30)(27,34,40,31)(35,41,48,44)(36,42,49,45)(38,46,50,43)(47,51,53,52);(22,25)(23,29)(24,32)(26,35)(27,36)(28,37)(30,41)(31,42)(33,44)(34,45)(38,47)(39,48)(40,49)(43,51)(46,52)(50,53);(22,26,28,39)(23,30,24,33)(25,35,37,48)(27,38,40,50)(29,41,32,44)(31,43,34,46)(36,47,49,53)(42,51,45,52);(22,27)(23,31)(24,34)(25,36)(26,38)(28,40)(29,42)(30,43)(32,45)(33,46)(35,47)(37,49)(39,50)(41,51)(44,52)(48,53)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55848);