Finite Group DatabasebetaFinite Group Databasebeta| order | 14912 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #11745400⋊C16 |
| derived, Sylow | C233 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #14272347 |
| commutator, hypocenter | C233 | C4×C16 |
| Frattini | C4 | C2×#14272347 |
| Fitting | C8×C233 | C8 |
| socle | C2×C233 | C4×C8 |
| prime radical | C2×D233 | C2×C8 |
| cosocle | #16836602 | C22 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3728 |
Polycyclic presentation:
2^6,233|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^221,g^b=g^89,g^c=g^144,g^d=g^232,g^e=g^232296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14912, 1642);