Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61109 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61111 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
2600 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,25)(17,29)(18,22)(19,36)(20,23)(21,28)(24,37)(26,43)(27,31)(30,32)(33,42)(34,41)(35,40)(38,45)(39,44);(14,16)(15,21)(17,23)(18,32)(19,29)(20,27)(22,39)(24,31)(25,36)(26,33)(28,37)(30,42)(34,44)(35,45)(38,41)(40,43);(14,17,20,21)(15,16,23,27)(18,30,35,38)(19,31,37,25)(22,26,40,44)(24,28,36,29)(32,42,45,41)(33,43,34,39);(14,18)(15,22)(16,26)(17,30)(19,34)(20,35)(21,38)(23,40)(24,42)(25,43)(27,44)(28,45)(29,32)(31,39)(33,37)(36,41);(15,23)(16,27)(22,40)(24,36)(26,44)(28,29)(32,45)(41,42)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54099);