Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18618 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18657 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3511 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
940 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)(14,15,19,23)(16,24,27,28)(17,21,18,22)(20,26,29,25)(30,31)(32,40)(33,36)(34,38)(35,39)(37,41)(42,45)(43,44);(14,16,19,27)(15,20,23,29)(17,25,18,26)(21,28,22,24)(31,36)(33,34)(37,44)(38,39)(40,45)(41,42);(14,17,19,18)(15,21,23,22)(16,25,27,26)(20,28,29,24)(30,32,35,43)(31,37,39,45)(33,41,34,42)(36,44,38,40);(14,17,19,18)(15,22,23,21)(16,26,27,25)(20,28,29,24)(30,33,35,34)(31,38,39,36)(32,41,43,42)(37,40,45,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11645);