Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C193 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C193 | C64 |
| prime radical | D193 | C32 |
| cosocle | #20260000 | C2 |
| LCS | G ▷ C193 | |
| UCS | C1 | |
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^125,g^b=g^185,g^c=g^64,g^d=g^43,g^e=g^112,g^f=g^19267 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽193) |
| maximal normal subgroup of | AGL(1,𝔽193) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 1684);