Finite Group DatabasebetaFinite Group Databasebeta| order | 14912 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C233 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #11745400 |
| commutator, hypocenter | C233 | C4×C16 |
| Frattini | C2×C4 | C2×#11745400 |
| Fitting | C2×C8×C233 | C4 |
| socle, prime radical | C22×C233 | C2×C8 |
| cosocle | C2×#14272338 | C22 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14912 |
Polycyclic presentation:
2^6,233|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^144,g^b=g^232,g^c=g^232992 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14912, 1435);