Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C8 |
| direct product | C8×#13095400 |
| derived, Sylow | C193 ⋊ C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #11715871 |
| commutator, hypocenter | C193 | C82 |
| Frattini | C2×C4 | C2×#11715871 |
| Fitting | C2×C8×C193 | C4 |
| socle, prime radical | C22×C193 | C42 |
| cosocle | C4×Dic193 | C22 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C2×C8 | |
74 conjugacy classes of subgroups.
832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 1389);