Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#27099 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C22⋊C4 ◁ G | |
700 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
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)(16,20)(17,19)(18,21)(22,23)(24,28)(25,27)(26,29)(30,31)(32,35)(33,36)(34,37)(38,45)(39,43)(40,42)(41,44);(14,16,18,17)(15,19,21,20)(22,24,26,25)(23,27,29,28)(30,32,33,39)(31,35,36,43)(34,38,41,40)(37,45,44,42);(14,16,18,17)(15,20,21,19)(22,25,26,24)(23,28,29,27)(31,36)(32,38)(34,41)(35,42)(39,40)(43,45);(14,17,18,16)(15,20,21,19)(23,29)(27,28)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 20087);