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×#19790 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | D42×C13 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
626 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)(14,15,18,21)(16,22,25,28)(17,26,27,20)(19,23,29,24)(30,31,34,38)(32,35,40,44)(33,36,41,37)(39,42,45,43);(14,16,18,25)(15,19,21,29)(17,23,27,24)(20,28,26,22)(30,32,34,40)(31,35,38,44)(33,39,41,45)(36,42,37,43);(31,36)(33,41)(35,42)(37,38)(39,45)(43,44);(16,23)(17,27)(19,28)(20,26)(22,29)(24,25)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12778);