Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C47×C128 ⋊ C2 |
| Sylow | C47 ⋊ M256 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C64 | C2×D47 |
| commutator, socle | C2×C47 | C2×C64 |
| Fitting | C47×C128 | C2 |
| prime radical | C2×D47 | C64 |
| cosocle | C47×C64 | C22 |
| hypercenter | C128 | D47 |
| hypocenter | C47 | M256 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C64 ◁ C128 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,47|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bh,i^b=i^463104 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 57478);