Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C193 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #15690569 |
| commutator, hypocenter | C193 | C2×C32 |
| Frattini | C2 | C2×#15690569 |
| Fitting | C4×C193 | C16 |
| socle | C2×C193 | C2×C16 |
| prime radical | C2×D193 | C16 |
| cosocle | #15690567 | C22 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C4 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,193|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^64,g^b=g^192,g^c=g^43,g^d=g^112,g^e=g^192112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 1678);