Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36733 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C2×C13×#120 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1790 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)(24,28)(25,29)(30,31)(32,38)(33,37)(34,35)(36,40)(39,44)(41,42)(43,45);(15,18)(19,21)(22,23,26,27)(24,29,28,25)(31,35)(36,38)(37,42)(43,44);(14,15)(16,19)(17,18)(20,21)(22,24)(23,25)(26,28)(27,29)(30,31)(32,36)(33,37)(34,35)(38,40)(39,43)(41,42)(44,45);(14,15)(16,19)(17,18)(20,21)(22,23)(24,25)(26,27)(28,29)(30,32)(31,36)(33,39)(34,40)(35,38)(37,43)(41,45)(42,44);(14,16)(15,19)(17,20)(18,21)(22,25)(23,24)(26,29)(27,28)(30,33,34,41)(31,37,35,42)(32,39,40,45)(36,43,38,44)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29721);