Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#23438 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| socle | C22×C13 | C2×#121 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
1922 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)(22,27)(23,28)(24,29)(25,33)(26,38)(31,46)(32,42)(34,41)(36,43)(37,45)(39,44)(40,48)(47,49);(15,17)(18,20)(19,25)(21,36)(22,32)(23,33)(24,34)(26,43)(27,30)(28,41)(29,42)(31,37)(35,46)(38,48)(39,47)(40,44)(45,49);(18,21)(19,26)(20,31)(22,37)(23,38)(24,39)(25,40)(27,35)(28,44)(29,45)(30,43)(32,47)(33,36)(34,48)(41,49)(42,46);(18,22,24,23)(19,27,29,28)(20,32,34,33)(21,37,39,38)(25,30,42,41)(26,35,45,44)(31,47,48,36)(40,43,46,49)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 16426);