Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C214 |
| direct product | C13×#62859 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
10986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 6 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(19,25)(20,26)(23,37)(27,34)(29,39)(32,45)(35,47)(44,49);(14,15)(16,17)(18,19,24,25)(20,21,26,33)(22,34,36,27)(23,28,37,38)(29,42,39,31)(30,32,40,45)(35,46,47,41)(43,49,48,44);(18,20)(19,21)(22,29)(23,30)(24,26)(25,33)(27,31)(28,32)(34,42)(35,43)(36,39)(37,40)(38,45)(41,44)(46,49)(47,48);(18,21)(19,26)(20,25)(22,31)(23,32)(24,33)(27,39)(28,40)(29,34)(30,38)(35,44)(36,42)(37,45)(41,48)(43,46)(47,49);(18,22,24,36)(19,27,25,34)(20,29,26,39)(21,31,33,42)(23,35,37,47)(28,41,38,46)(30,43,40,48)(32,44,45,49);(18,23)(19,28)(20,30)(21,32)(22,35)(24,37)(25,38)(26,40)(27,41)(29,43)(31,44)(33,45)(34,46)(36,47)(39,48)(42,49)1066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 55847);