Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C41 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#4223 |
| commutator, socle | C2×C41 | C22×C4 |
| Fitting | Q8×C41 | C4 |
| prime radical | #10620310 | C2 |
| cosocle | Dic41 | C23 |
| hypercenter | Q8 | #4223 |
| hypocenter | C41 | #131 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^5,41|a^2=d,d^2=e,f^a=f^32,c^b=ce,f^b=f^40,f^c=f^40,f^d=f^4070 conjugacy classes — view the full character table.
| maximal subgroup of | #14581379, #14581380, #14581381, … |
| maximal normal subgroup of | #14581379, #14581380, #14581381, … |
| maximal quotient of | #14581301, #14581311, #14581343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 234);