Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24421 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3585 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1310 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)(14,15,20,34,19,21,18,24)(16,25,33,22,28,36,26,35)(17,29,31,38,32,23,30,39)(27,40,41,44,42,45,43,37);(15,21)(16,26)(18,20)(22,36)(23,29)(25,35)(27,41)(28,33)(30,31)(37,45)(40,44)(42,43);(14,16)(15,22)(17,27)(18,33)(19,28)(20,26)(21,35)(23,37)(24,36)(25,34)(29,44)(30,41)(31,43)(32,42)(38,40)(39,45);(14,17)(15,23)(16,27)(18,31)(19,32)(20,30)(21,29)(22,37)(24,39)(25,40)(26,41)(28,42)(33,43)(34,38)(35,44)(36,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17409);