Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C257 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C257 | C32 |
| LCS | G ▷ C257 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,257|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^136,f^b=f^249,f^c=f^64,f^d=f^241,f^e=f^25640 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22551693, #30657872 |
| maximal normal subgroup of | C2×#22551693, #30657872 |
| maximal quotient of | #30657870, C2×#22551693 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 247);