Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C42 |
| direct product | D13×#2500 |
| Fitting | C13×#2500 ⋊ C2 |
| Sylow | C13 ⋊ C2×#2500 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D13 |
| commutator, socle, cosocle | C23×C13 | C25 |
| Fitting | C13×#2500 | C2 |
| prime radical | C2×D13×#121 | C2 |
| hypercenter | #2500 | D13 |
| hypocenter | C13 | C2×#2500 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #2500 | |
3222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 339154);