Finite Group DatabasebetaFinite Group Databasebeta| order | 5648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C353 ⋊ C2 |
| Sylow | C353 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D353 |
| commutator, socle | C2×C353 | C2×C4 |
| Fitting | C8×C353 | C2 |
| hypercenter | C8 | D353 |
| hypocenter | C353 | M16 |
| LCS | G ▷ C2×C353 ▷ C353 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,353|a^2=c,c^2=d,b^a=bd,e^b=e^3521418 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M16×D353, C2×#19150720, #26014998, … |
| maximal normal subgroup of | M16×D353, C2×#19150720, #26014998, … |
| maximal quotient of | #26014902, #26014904, #26014921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5648, 23);