Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33539 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#33539 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
1130 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)(16,27)(17,31)(18,26)(19,25)(20,23)(21,28)(22,29)(24,34)(30,42)(32,43)(33,37)(35,41)(36,40)(38,44)(39,45);(14,16)(15,21)(17,32)(18,29)(19,36)(20,30)(22,37)(23,38)(24,40)(25,39)(26,43)(27,31)(28,34)(33,44)(35,45)(41,42);(14,16)(15,22)(17,28)(18,36)(19,29)(20,30)(21,37)(23,40)(24,38)(25,42)(26,27)(31,43)(32,34)(33,45)(35,44)(39,41);(15,23)(21,38)(22,40)(24,37)(25,26)(27,42)(31,41)(39,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26527);