Finite Group DatabasebetaFinite Group Databasebeta| order | 5648 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C353 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | D353 |
| commutator, hypocenter | C353 | C16 |
| Fitting | C8×C353 | C2 |
| socle | C2×C353 | C8 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C8 | |
10 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,353|a^2=b,b^2=c,c^2=d,e^a=e^3521424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D353, C2×#19150712, #26014931, … |
| maximal normal subgroup of | C16×D353, C2×#19150712, #26014931, … |
| maximal quotient of | #26014898, C2×#19150712 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5648, 15);