Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33854 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33854 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C13×#443 ◁ G | |
656 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)(17,29)(18,19)(22,39)(23,41)(24,43)(25,38)(27,44)(28,34)(30,35)(32,33)(36,40)(37,42);(14,15)(16,22)(17,30)(18,24)(19,35)(20,25)(21,29)(23,27)(26,40)(28,41)(31,36)(32,38)(33,43)(34,37)(39,44)(42,45);(14,16)(15,22)(17,27)(18,34)(19,26)(20,28)(21,36)(23,30)(24,37)(25,41)(29,31)(32,45)(33,44)(35,40)(38,42)(39,43);(14,16)(15,23)(17,31)(18,26)(19,34)(20,28)(21,37)(22,30)(24,36)(25,39)(27,29)(32,44)(33,45)(35,42)(38,40)(41,43)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26842);