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×#18672 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
906 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)(16,22)(17,25)(18,20)(19,24)(21,27)(23,29)(26,28)(31,36)(32,40)(33,34)(38,39)(41,42)(43,44);(14,16,18,23)(15,19,20,28)(17,26,27,24)(21,29,25,22)(30,31,35,39)(32,37,41,45)(33,36,34,38)(40,43,42,44);(30,32,35,41)(31,37,39,45)(33,40,34,42)(36,43,38,44);(15,20)(16,23)(21,25)(24,26)(30,33,35,34)(31,38,39,36)(32,40,41,42)(37,44,45,43)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11660);