Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×D41 |
| Fitting | C16×C41 ⋊ C2 |
| derived, Sylow | C41 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | D41 |
| commutator, hypocenter | C41 | C2×C16 |
| Frattini | C8 | C2×D41 |
| Fitting | C16×C41 | C2 |
| socle | C2×C41 | C2×C8 |
| prime radical | C2×D41 | C8 |
| cosocle | C8×C41 | C22 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C16 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D41, #14580169, C2×C16×D41, … |
| maximal normal subgroup of | C32×D41, #14580169, C2×C16×D41, … |
| maximal quotient of | C16×Dic41, #14580115, #14580154, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 83);