Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33569 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C24×C13 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G | |
1082 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26)(17,23)(18,31)(19,34)(20,25)(21,27)(22,30)(24,36)(28,41)(29,44)(32,38)(33,40)(35,37)(39,45)(42,43);(14,16)(15,21)(17,27)(18,32)(19,35)(20,28)(22,37)(23,41)(24,39)(25,38)(26,31)(29,36)(30,45)(33,43)(34,42)(40,44);(14,17,20,18)(15,22,25,40)(16,27,28,32)(19,33,36,30)(21,37,38,44)(23,24,31,34)(26,42,41,39)(29,45,35,43);(16,28)(21,38)(26,41)(27,32)(29,35)(37,44)(39,42)(43,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26557);