Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32753 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G | |
614 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)(16,18)(17,19)(20,21)(22,23,25,28)(24,27,29,26)(30,31)(32,39)(33,42)(34,38)(35,37)(36,41)(40,45)(43,44);(14,16)(15,18)(17,20)(19,21)(22,24,25,29)(23,26,28,27)(32,40)(33,35)(36,44)(37,42)(39,45)(41,43);(15,19)(18,21)(22,24)(23,27)(25,29)(26,28)(30,32,34,41)(31,36,38,39)(33,40,35,43)(37,45,42,44);(16,20)(18,21)(24,29)(26,27)(30,33,34,35)(31,37,38,42)(32,40,41,43)(36,45,39,44)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25741);