Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C41 ⋊ C2 |
| Sylow | C41 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D41 |
| commutator, socle, cosocle | C22×C41 | C23 |
| Fitting | C4⋊C4×C41 | C2 |
| prime radical | C2×D164 | C2 |
| hypercenter | C4⋊C4 | D41 |
| hypocenter | C41 | #123 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^5,41|c^2=d,b^a=bd,c^a=ce,f^a=f^40,f^b=f^40214 conjugacy classes — view the full character table.
| maximal subgroup of | #123×D41, C2×#13050149, #14580845, … |
| maximal normal subgroup of | #123×D41, C2×#13050149, #14580845, … |
| maximal quotient of | #14580198, #14580207, #14580214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 131);