Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#18069 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C22×D4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C22×C13 | C2×C4×D4 |
| prime radical | C13×#466 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C4×C13×M16 ◁ G | |
600 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)(16,23)(17,21)(18,26)(19,22)(20,24)(25,28)(27,29)(30,31,35,38,34,37,43,45)(32,39,41,42,40,36,44,33);(14,16)(15,20)(17,24)(18,27)(19,25)(21,28)(22,29)(23,26)(30,32)(31,36)(33,38)(34,40)(35,41)(37,39)(42,45)(43,44);(30,33,35,39,34,42,43,36)(31,32,38,41,37,40,45,44);(14,17,19,18)(15,21,22,26)(16,24,25,27)(20,28,29,23)(32,40)(33,42)(36,39)(41,44)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11057);