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×#62861 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6854 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)(14,15,17,19)(16,18,20,21)(22,23)(24,29)(25,35)(26,30)(27,41)(28,32)(31,42)(33,43)(34,37)(36,38)(39,51)(40,46)(44,48)(45,52)(47,49)(50,53);(14,15)(16,18)(17,19)(20,21)(22,24,28,35)(23,29,32,25)(26,38,40,33)(27,34,42,48)(30,36,46,43)(31,44,41,37)(39,50,52,47)(45,49,51,53);(22,25)(23,24)(26,36)(27,37)(28,29)(30,33)(31,34)(32,35)(38,46)(39,49)(40,43)(41,48)(42,44)(45,47)(50,51)(52,53);(22,23)(24,29)(25,35)(26,30)(27,31)(28,32)(33,43)(34,44)(36,38)(37,48)(39,45)(40,46)(41,42)(47,53)(49,50)(51,52);(22,26,28,40)(23,30,32,46)(24,33,35,38)(25,36,29,43)(27,39,42,52)(31,45,41,51)(34,47,48,50)(37,49,44,53);(14,16,17,20)(15,18,19,21)(22,27)(23,31)(24,34)(25,37)(26,39)(28,42)(29,44)(30,45)(32,41)(33,47)(35,48)(36,49)(38,50)(40,52)(43,53)(46,51)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55849);