Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36822 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C13×#2404 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1792 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(16,20)(19,21)(23,27)(25,29)(30,31,34,37)(32,38,40,35)(33,36,41,43)(39,44,45,42);(15,18)(19,21)(23,27)(24,28)(30,32,34,40)(31,35,37,38)(33,39,41,45)(36,42,43,44);(14,15)(16,19)(17,18)(20,21)(22,23,26,27)(24,25,28,29)(30,32)(31,35)(33,39)(34,40)(36,42)(37,38)(41,45)(43,44);(14,15)(16,19)(17,18)(20,21)(22,24,26,28)(23,25,27,29)(30,31)(32,35)(33,36)(34,37)(38,40)(39,42)(41,43)(44,45);(14,16)(15,19)(17,20)(18,21)(22,25)(23,28)(24,27)(26,29)(30,33,34,41)(31,36,37,43)(32,39,40,45)(35,42,38,44)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29810);