Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C23×#13095402 |
| Fitting, socle | C23×C193 ⋊ C8 |
| derived, Sylow | C193 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #13095402 |
| commutator, hypocenter | C193 | C23×C8 |
| Frattini | C1 | G |
| Fitting, socle | C23×C193 | C8 |
| prime radical | C23×D193 | C4 |
| cosocle | #11715871 | C24 |
| LCS | G ▷ C193 | |
| UCS | C1 ◁ C23 | |
338 conjugacy classes of subgroups.
256 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 1672);