Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| isoclinism | isoclinic class of Dic106 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic106 |
| Sylow | C53 ⋊ C23×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D53 |
| commutator, cosocle | C2×C53 | C25 |
| Frattini | C2 | C24×D53 |
| Fitting | C23×C4×C53 | C2 |
| socle, prime radical | C24×C53 | C22 |
| hypercenter | C23×C4 | D53 |
| hypocenter | C53 | C23×Q8 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
872 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 1373);