Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C41 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #4223 |
| commutator, hypocenter | C41 | C2×C16 |
| Frattini | C4 | C2×#4223 |
| Fitting | C8×C41 | C4 |
| socle | C2×C41 | C2×C8 |
| prime radical | C2×D41 | C8 |
| cosocle | #66491 | C22 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^5,41|a^2=c,c^2=d,d^2=e,f^a=f^32,f^b=f^40,f^c=f^40112 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#4223, #14581223, #14581248, … |
| maximal normal subgroup of | C16×#4223, #14581223, #14581248, … |
| maximal quotient of | #14581222, #14581231, #14581257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 219);