Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
1648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,30)(21,35)(22,29)(23,28)(24,33)(25,37)(26,36)(27,40)(31,46)(32,41)(34,43)(38,45)(39,42)(44,48)(47,49);(18,20,23,34)(19,24,28,42)(21,32,37,47)(22,39,40,33)(25,44,35,46)(26,41,45,49)(27,43,29,30)(31,36,48,38);(15,17)(18,21)(19,25)(20,31)(22,36)(23,37)(24,41)(26,27)(28,35)(29,45)(30,44)(32,39)(33,47)(34,48)(38,40)(42,49)(43,46);(18,21)(19,26)(20,32)(22,38)(23,37)(24,41)(25,27)(28,45)(29,35)(30,46)(31,39)(33,48)(34,47)(36,40)(42,49)(43,44)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16877);