Finite Group DatabasebetaFinite Group Databasebeta| order | 12352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C193 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D193 |
| commutator | C22×C193 | C22×C4 |
| Fitting, prime radical | C25×C193 | C2 |
| socle, cosocle | C23×C193 | C23 |
| hypercenter | C25 | D193 |
| hypocenter | C193 | #379 |
| LCS | G ▷ C22×C193 ▷ C193 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,193|a^2=f,b^a=bd,c^a=ce,g^a=g^1923100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12352, 405);