Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#29085 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C4×C13×C4⋊C4 ◁ G | |
684 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,18)(16,20,21,19)(22,23,25,27)(24,28,29,26)(30,31,34,38)(32,36,42,35)(33,39,40,37)(41,44,43,45);(15,18)(19,20)(22,24,25,29)(23,26,27,28)(30,32,40,41,34,42,33,43)(31,35,37,45,38,36,39,44);(23,27)(26,28)(30,32,34,42)(31,36,38,35)(33,41,40,43)(37,45,39,44);(14,16,17,21)(15,19,18,20)(23,27)(26,28)(30,33,34,40)(31,37,38,39)(32,41,42,43)(35,44,36,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 22073);