Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#19417 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
608 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)(14,15,18,21)(16,22,25,29)(17,26,23,20)(19,27,28,24)(30,31,35,39)(32,36,41,45)(33,38,34,43)(37,42,44,40);(14,16,23,27,18,25,17,24)(15,19,26,29,21,28,20,22)(30,32)(31,36)(33,42)(34,40)(35,41)(37,43)(38,44)(39,45);(30,32)(31,37)(33,40)(34,42)(35,41)(36,43)(38,45)(39,44);(30,33,35,34)(31,38,39,43)(32,40,41,42)(36,37,45,44)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12405);