Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q8×C41 ⋊ C2 |
| Sylow | C41 ⋊ #124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D41 |
| commutator, socle, cosocle | C22×C41 | C23 |
| Fitting | C2×Q8×C41 | C2 |
| prime radical | C2×D164 | C2 |
| hypercenter | C2×Q8 | D41 |
| hypocenter | C41 | #124 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^5,41|b^2=e,c^2=d,b^a=bd,c^a=ce,f^a=f^40,f^b=f^40,f^c=f^40214 conjugacy classes — view the full character table.
| maximal subgroup of | #14580132, #14580509, #14580511, … |
| maximal normal subgroup of | #14580132, #14580509, #14580511, … |
| maximal quotient of | #14580201, #14580226, #14580237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 135);