Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36924 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| prime radical | C2×C13×#121 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
1610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
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)(25,28)(30,31,35,39)(32,37,33,36)(34,42,43,38)(40,44,41,45);(15,18)(19,21)(23,27)(24,29)(30,32,35,33)(31,36,39,37)(34,41,43,40)(38,45,42,44);(14,15)(16,19)(17,18)(20,21)(22,23,26,27)(24,28,29,25)(30,33,35,32)(31,37,39,36)(34,41,43,40)(38,45,42,44);(14,15)(16,19)(17,18)(20,21)(22,24)(23,28)(25,27)(26,29)(30,34,35,43)(31,38,39,42)(32,40,33,41)(36,44,37,45);(14,16)(15,19)(17,20)(18,21)(22,25,26,28)(23,24,27,29)(30,31)(32,36)(33,37)(34,38)(35,39)(40,44)(41,45)(42,43)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29912);