Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×#20260000 |
| Fitting, socle | C2×C193 ⋊ C32 |
| derived, Sylow | C193 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #20260000 |
| commutator, hypocenter | C193 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C193 | C32 |
| prime radical | C2×D193 | C16 |
| cosocle | #15690569 | C22 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C2 | |
34 conjugacy classes of subgroups.
76 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 1683);