Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19037 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
812 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)(14,15,19,22)(16,23,26,29)(17,21,18,27)(20,24,28,25)(30,31,35,32)(33,40,41,45)(34,39,44,37)(36,43,38,42);(14,16)(15,20)(17,25)(18,24)(19,26)(21,29)(22,28)(23,27)(30,32,35,31)(33,38,41,36)(34,37,44,39)(40,43,45,42);(14,15)(16,20)(17,21)(18,27)(19,22)(23,24)(25,29)(26,28)(30,33)(31,36)(32,38)(34,43)(35,41)(37,45)(39,40)(42,44);(14,17,19,18)(15,21,22,27)(16,24,26,25)(20,23,28,29)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12025);