Finite Group DatabasebetaFinite Group Databasebeta| order | 5648 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C353 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C353 | C16 |
| LCS | G ▷ C353 | |
| UCS | C1 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,353|a^2=b,b^2=c,c^2=d,e^a=e^304,e^b=e^283,e^c=e^311,e^d=e^35238 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#19150751, #26015093 |
| maximal normal subgroup of | C2×#19150751, #26015093 |
| maximal quotient of | #26015091, C2×#19150751 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5648, 54);