Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36816 |
| 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 | |
1800 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)(30,31,35,38)(32,39,33,36)(34,42,43,37)(40,44,41,45);(15,18)(19,21)(23,27)(24,28)(30,32,35,33)(31,36,38,39)(34,40,43,41)(37,44,42,45);(14,15)(16,19)(17,18)(20,21)(22,23,26,27)(24,25,28,29)(30,33,35,32)(31,36,38,39)(34,41,43,40)(37,44,42,45);(14,15)(16,19)(17,18)(20,21)(22,24,26,28)(23,25,27,29)(30,31)(32,39)(33,36)(34,37)(35,38)(40,45)(41,44)(42,43);(14,16)(15,19)(17,20)(18,21)(22,25)(23,28)(24,27)(26,29)(30,34,35,43)(31,37,38,42)(32,40,33,41)(36,44,39,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29804);