Finite Group DatabasebetaFinite Group Databasebeta| order | 1328 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D83 |
| unambiguous semidirect product | C83⋊C24 |
| unambiguous semidirect product | (C2×C83)⋊C23 |
| Fitting, socle | C23×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D83 |
| commutator, cosocle, hypocenter | C83 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C83 | C2 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 664 |
344 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D83, C2×(C2×D83)⋊C4, #14581760, … |
| maximal normal subgroup of | C22⋊C4×D83, C2×(C2×D83)⋊C4, #14581760, … |
| maximal quotient of | C22×C4×D83, C23×Dic83, C2×D4×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1328, 42);