Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C113 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #11744762 |
| commutator, hypocenter | C113 | C2×C64 |
| Frattini | C8 | C2×#11744762 |
| Fitting | C16×C113 | C8 |
| socle | C2×C113 | C2×C32 |
| prime radical | C2×D113 | C32 |
| cosocle | #16813672 | C22 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C16 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7232 |
Polycyclic presentation:
2^7,113|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^18,h^b=h^112,h^c=h^98,h^d=h^112352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 21613);