Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18424 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1020 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
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)(16,26)(17,20)(18,24)(19,33)(21,25)(22,28)(23,35)(27,36)(29,39)(30,42)(31,44)(32,37)(34,38)(40,45)(41,43);(14,16,20,30)(15,22,17,27)(18,28,19,36)(21,31,38,29)(23,39,32,44)(24,42,33,26)(25,41,34,40)(35,43,37,45);(14,17,20,15)(16,27,30,22)(18,23,19,32)(21,34,38,25)(24,37,33,35)(26,43,42,45)(28,39,36,44)(29,41,31,40);(14,18,20,19)(15,23,17,32)(16,28,30,36)(21,35,38,37)(22,39,27,44)(24,34,33,25)(26,41,42,40)(29,45,31,43)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11412);