Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#19040 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
872 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)(32,39)(33,37)(34,43)(35,38)(36,41)(40,44)(42,45);(14,15,19,22)(16,21,24,28)(17,25,18,20)(23,29,26,27)(30,32,35,42)(31,36,38,44)(33,41,34,40)(37,45,43,39);(14,16)(15,21)(17,23)(18,26)(19,24)(20,27)(22,28)(25,29)(30,31)(32,36)(33,37)(34,43)(35,38)(39,40)(41,45)(42,44);(15,22)(20,25)(21,28)(27,29)(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, 12028);