Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33531 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33533 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
1102 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)(16,25)(17,22)(18,31)(19,29)(20,24)(21,27)(23,34)(26,42)(28,43)(30,33)(32,37)(35,44)(36,40)(38,41)(39,45);(14,16)(15,21)(17,26)(18,32)(19,36)(20,28)(22,37)(23,40)(24,38)(25,31)(27,34)(29,39)(30,41)(33,42)(35,45)(43,44);(14,15)(16,21)(17,29)(18,33)(19,22)(20,24)(23,35)(25,41)(26,39)(27,43)(28,38)(30,31)(32,42)(34,44)(36,37)(40,45);(14,17,20,19)(15,22,24,29)(16,26,28,36)(18,30,35,34)(21,37,38,39)(23,31,33,44)(25,42,43,40)(27,32,41,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26521);