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×#33541 |
| 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 | |
1104 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)(15,21)(16,26)(17,19)(18,29)(22,37)(23,30)(24,35)(25,36)(27,42)(28,33)(31,32)(34,38)(39,45)(40,43);(14,15)(16,22)(17,23)(18,30)(19,24)(20,25)(21,29)(26,38)(27,43)(28,40)(31,36)(32,35)(33,39)(34,41)(37,42)(44,45);(14,16)(15,22)(17,26)(18,27)(19,33)(20,28)(21,34)(23,38)(24,39)(25,40)(29,41)(30,43)(31,44)(32,42)(35,37)(36,45);(14,17,20,19)(15,23,25,24)(16,26,28,33)(18,29,32,31)(21,35,36,30)(22,38,40,39)(27,41,42,44)(34,37,45,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26529);