Finite Group DatabasebetaFinite Group Databasebeta| order | 1312 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#66493 |
| Sylow | C41 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#4223 |
| commutator | C2×C41 | C2×C8 |
| Fitting, prime radical | C23×C41 | C4 |
| socle | C22×C41 | C2×C4 |
| cosocle | C2×Dic41 | C22 |
| hypercenter | C23 | #4223 |
| hypocenter | C41 | C22⋊C8 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C23 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^5,41|a^2=d,d^2=e,b^a=bc,f^a=f^32,f^d=f^40100 conjugacy classes — view the full character table.
| maximal subgroup of | #14581179, #14581180, #14581181, … |
| maximal normal subgroup of | #14581179, #14581180, #14581181, … |
| maximal quotient of | #14581179, #14581181, D4⋊#66493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1312, 202);