Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19022 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3559 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
892 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)(15,20)(16,23)(17,18)(22,25)(24,26)(27,29)(30,31,35,33)(32,38,40,45)(34,42,44,37)(36,43,39,41);(14,15)(16,21)(17,25)(18,20)(19,22)(23,29)(24,28)(26,27)(30,32)(31,36)(33,39)(34,43)(35,40)(37,45)(38,42)(41,44);(14,16,19,24)(15,21,22,28)(17,23,18,26)(20,27,25,29)(30,33,35,31)(32,39,40,36)(34,37,44,42)(38,43,45,41);(15,22)(20,25)(21,28)(27,29)(32,40)(36,39)(38,45)(41,43)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12010);