Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33595 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33595 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#459 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
706 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)(15,20)(16,24)(17,28)(18,29)(21,35)(22,33)(23,39)(25,30)(26,41)(27,42)(31,43)(32,37)(36,40)(38,45);(14,15,17,20,19,22,28,33)(16,21,25,32,27,36,26,38)(18,23,29,34,31,39,43,44)(24,37,41,35,42,45,30,40);(14,16)(15,21)(17,25)(18,30)(19,27)(20,32)(22,36)(23,40)(24,29)(26,28)(31,41)(33,38)(34,37)(35,39)(42,43)(44,45);(15,22)(20,33)(21,36)(23,39)(32,38)(34,44)(35,40)(37,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26583);