Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22455 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#22455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | D4×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#576 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1378 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)(16,24)(17,29,31,21)(18,32)(19,23)(20,27)(22,33)(25,39,42,38)(26,36)(28,35)(30,37,45,44)(34,41,43,40);(14,16)(15,20)(17,25)(18,26)(19,28)(21,34)(22,35)(23,36)(24,32)(27,33)(29,43)(30,40)(31,42)(37,39)(38,44)(41,45);(14,17)(15,21)(16,25)(18,30)(19,31)(20,34)(22,37)(23,29)(24,38)(26,40)(27,41)(28,42)(32,44)(33,45)(35,39)(36,43);(16,26)(18,33)(20,35)(22,32)(24,36)(25,40)(27,28)(30,45)(34,39)(37,44)(38,43)(41,42)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15443);