Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18240 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
1056 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
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)(17,27)(21,32)(22,31)(23,28)(25,36)(29,41)(33,38)(34,43)(35,42)(39,40)(44,45);(14,15)(16,21)(17,28)(18,23)(19,22)(20,27)(24,33)(25,38)(26,34)(29,42)(30,35)(31,41)(32,36)(37,45)(39,43)(40,44);(16,24)(17,29)(20,31)(21,33)(25,39)(26,37)(27,41)(28,42)(32,44)(34,45)(36,40)(38,43);(14,16,19,26)(15,21,22,34)(17,25,29,40)(18,24,30,37)(20,32,31,43)(23,33,35,45)(27,36,41,39)(28,38,42,44)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11228);