Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C27 |
| direct product | C13×#36693 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C13 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C13 |
| socle | C23×C13 | C25 |
| prime radical | C13×#392 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C13 ◁ G | |
1536 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)(14,15,18,20)(16,19,17,21)(22,23)(24,26)(25,27)(28,29)(30,31)(32,36)(33,37)(34,35)(38,41)(39,43)(40,42)(44,45);(14,16,18,17)(15,19,20,21)(22,24,25,29)(23,26,27,28)(31,35)(36,41)(37,42)(43,45);(15,20)(19,21)(22,23)(24,28)(25,27)(26,29)(30,32)(31,36)(33,39)(34,38)(35,41)(37,43)(40,44)(42,45);(14,17,18,16)(15,21,20,19)(23,27)(26,28)(32,38)(36,41)(39,44)(43,45);(30,33,34,40)(31,37,35,42)(32,39,38,44)(36,43,41,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 29681);