Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#18414 |
| 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 ◁ C23×C4×C13 ◁ G | |
1042 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)(16,24)(17,27)(21,33)(22,31)(23,28)(25,37)(26,40)(29,42)(32,35)(34,44)(36,43)(38,39)(41,45);(14,15)(16,21)(17,28)(18,23)(19,22)(20,27)(24,35)(25,34)(26,41)(29,43)(30,36)(31,42)(32,39)(33,40)(37,45)(38,44);(16,25)(17,29)(20,31)(21,34)(24,37)(26,40)(27,42)(28,43)(32,44)(33,41)(35,45)(38,39);(14,16)(15,21)(17,26)(18,25)(19,24)(20,32)(22,35)(23,34)(27,39)(28,41)(29,38)(30,37)(31,33)(36,45)(40,42)(43,44)481 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11402);