Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #41×C41 ⋊ C2 |
| Sylow | C41 ⋊ AGL(1,ℤ/8) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×C22⋊D41 |
| commutator, cosocle | C4×C41 | C23 |
| Frattini | C4 | C22×D41 |
| Fitting | #41×C41 | C2 |
| socle | C2×C41 | C2×D4 |
| hypercenter | #41 | D41 |
| hypocenter | C41 | AGL(1,ℤ/8) |
| LCS | G ▷ C4×C41 ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #41 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^5,41|d^2=e,b^a=bd,c^a=ce,d^a=de,d^b=de,f^b=f^40211 conjugacy classes — view the full character table.
| maximal subgroup of | #14580504, #14580505, #14580509, … |
| maximal normal subgroup of | #14580504, #14580505, #14580509, … |
| maximal quotient of | #14580337, #14580340, #14580379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 171);