Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19755 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#19814 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C2×C13×D8 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
590 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)(15,19)(17,25)(20,26)(21,22)(23,29)(27,28)(30,31,34,37)(32,38,40,45)(33,41,43,36)(35,42,44,39);(14,15)(16,20)(17,21)(18,22)(19,25)(23,27)(24,28)(26,29);(14,16,18,24)(15,20,22,28)(17,23,25,29)(19,26,21,27)(30,32,34,40)(31,35,37,44)(33,42,43,39)(36,45,41,38);(15,21)(17,25)(19,22)(20,27)(23,29)(26,28)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12802);