Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19024 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#3558 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
948 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 832 |
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)(16,24)(17,21)(18,22)(19,23)(20,25)(26,28)(27,29)(30,31,35,38)(32,39,42,45)(33,37,34,43)(36,40,44,41);(14,16)(15,20)(17,27)(18,25)(19,26)(21,24)(22,28)(23,29)(30,32)(31,36)(33,41)(34,40)(35,42)(37,45)(38,44)(39,43);(14,16)(15,20)(17,25)(18,27)(19,26)(21,28)(22,24)(23,29)(30,31)(32,36)(33,37)(34,43)(35,38)(39,40)(41,45)(42,44);(14,17,19,18)(15,21,23,22)(16,25,26,27)(20,28,29,24)(30,33,35,34)(31,37,38,43)(32,40,42,41)(36,39,44,45)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12012);