Finite Group DatabasebetaFinite Group Databasebeta| order | 3392 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4×D53 |
| Fitting | C23×C4×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D53 |
| commutator, hypocenter | C53 | C24×C4 |
| Frattini | C2 | C24×D53 |
| Fitting | C23×C4×C53 | C2 |
| socle | C24×C53 | C22 |
| prime radical | C24×D53 | C2 |
| cosocle | C2×C53 | C25 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23×C4 | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
896 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3392, 1367);