Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C193 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #15690569 |
| commutator, hypocenter | C193 | C64 |
| Fitting | C4×C193 | C16 |
| socle, prime radical | C2×C193 | C32 |
| cosocle | #20259989 | C2 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C4 | |
14 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,193|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^64,g^b=g^43,g^c=g^112,g^d=g^192112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 1673);