Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D8×D41 |
| Fitting | D8×C41 ⋊ C2 |
| Sylow | C41 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D41 |
| commutator, cosocle | C4×C41 | C23 |
| Frattini | C4 | C22×D41 |
| Fitting | D8×C41 | C2 |
| socle | C2×C41 | C2×D4 |
| hypercenter | D8 | D41 |
| hypocenter | C41 | C2×D8 |
| LCS | G ▷ C4×C41 ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | D16×D41, SD32×D41, #14580770, … |
| maximal normal subgroup of | D16×D41, SD32×D41, #14580770, … |
| maximal quotient of | #102×D41, #107×D41, #14580416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 155);