Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#18433 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#121 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
872 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(17,24)(19,25)(20,27)(22,28)(30,31,36,33)(32,40,43,45)(34,39,35,38)(37,44,41,42);(14,15)(16,19)(17,20)(18,21)(22,26)(23,25)(24,27)(28,29)(30,32,36,43)(31,37,33,41)(34,42,35,44)(38,40,39,45);(14,16)(15,19)(17,22)(18,23)(20,26)(21,25)(24,28)(27,29)(30,33,36,31)(32,41,43,37)(34,38,35,39)(40,44,45,42);(14,17,18,24)(15,20,21,27)(16,22,23,28)(19,26,25,29)(30,34,36,35)(31,38,33,39)(32,42,43,44)(37,40,41,45)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11421);