Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17577 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#17594 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3444 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C42×C13 ◁ G | |
1014 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)(16,22,24,19)(17,25)(18,21)(20,26)(23,27,29,28)(30,31)(32,40)(33,39)(34,37)(35,38)(36,41)(42,45)(43,44);(14,16)(15,19)(17,23)(18,24)(20,27)(21,22)(25,28)(26,29)(30,32)(31,36)(33,41)(34,43)(35,42)(37,40)(38,44)(39,45);(30,33,35,34)(31,37,38,39)(32,41,42,43)(36,40,44,45);(14,17,18,26)(15,20,21,25)(16,23,24,29)(19,27,22,28)(31,38)(36,44)(37,39)(40,45)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10582);