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 | C4 | C22×D41 |
| commutator, socle | C2×C41 | C22×C4 |
| Fitting, prime radical | #41×C41 | C2 |
| cosocle | C4×C41 | C23 |
| hypercenter | #41 | D41 |
| hypocenter | C41 | #131 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^5,41|a^2=d,d^2=e,f^a=f^40,c^b=ce220 conjugacy classes — view the full character table.
| maximal subgroup of | #14580450, #14580453, #14580455, … |
| maximal normal subgroup of | #14580450, #14580453, #14580455, … |
| maximal quotient of | #14580292, #14580303, #14580363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 153);