Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | D42×#261 |
| Fitting | D42×C13 ⋊ C4 |
| Sylow | C13 ⋊ C4×D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×#261 |
| commutator, socle | C22×C13 | C24×C4 |
| Fitting | D42×C13 | C4 |
| prime radical | D42×D13 | C2 |
| cosocle | C22×D13 | C25 |
| hypercenter | D42 | #261 |
| hypocenter | C13 | C4×D42 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ D42 | |
4804 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#3484, #261×#3498 |
| maximal normal subgroup of | #261×#3484, #261×#3498 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1114267);