Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#32787 |
| 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 ◁ C22×C42×C13 ◁ G | |
672 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)(22,23,25,26)(24,27,29,28)(30,31,35,38)(32,39,33,36)(34,37,42,45)(40,44,41,43);(14,16)(15,18)(17,20)(19,21)(22,24)(23,27)(25,29)(26,28)(30,32,35,33)(31,36,38,39)(34,41,42,40)(37,44,45,43);(15,19)(18,21)(23,26)(24,28)(27,29)(30,33,35,32)(31,36,38,39)(34,40,42,41)(37,44,45,43);(16,20)(18,21)(24,29)(27,28)(30,34,35,42)(31,37,38,45)(32,40,33,41)(36,43,39,44)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25775);