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×#62848 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
10962 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)(19,24)(22,34)(25,28)(26,35)(30,44)(33,45)(37,40)(43,49);(14,15)(16,17)(21,32)(26,35)(29,42)(33,45)(37,40)(39,46)(43,49)(47,48);(18,19,23,24)(20,28,31,25)(21,26,32,35)(22,27,34,36)(29,40,42,37)(30,41,44,38)(33,39,45,46)(43,48,49,47);(18,20,23,31)(19,25,24,28)(21,29,32,42)(22,30,34,44)(26,37,35,40)(27,38,36,41)(33,43,45,49)(39,47,46,48);(18,21)(19,26)(20,29)(22,33)(23,32)(24,35)(25,37)(27,39)(28,40)(30,43)(31,42)(34,45)(36,46)(38,47)(41,48)(44,49);(18,22)(19,27)(20,30)(21,33)(23,34)(24,36)(25,38)(26,39)(28,41)(29,43)(31,44)(32,45)(35,46)(37,47)(40,48)(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, 55836);