Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C41 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D41 |
| commutator, socle, cosocle | C22×C41 | C23 |
| Fitting | C22×C4×C41 | C2 |
| prime radical | C23×C41 | C22 |
| hypercenter | C22×C4 | D41 |
| hypocenter | C41 | C22⋊Q8 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^5,41|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=f^40334 conjugacy classes — view the full character table.
| maximal subgroup of | #14580072, #14580074, #14580487, … |
| maximal normal subgroup of | #14580072, #14580074, #14580487, … |
| maximal quotient of | #14580196, #14580209, #14580220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 125);