Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C193 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #13095402 |
| commutator, hypocenter | C193 | C4×C16 |
| Frattini | C4 | C2×#13095402 |
| Fitting | C8×C193 | C8 |
| socle | C2×C193 | C4×C8 |
| prime radical | C2×D193 | C2×C8 |
| cosocle | #15690563 | C22 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C8 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,193|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^43,g^b=g^81,g^c=g^112,g^d=g^192,g^e=g^192256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 1642);