Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C257 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D257 |
| commutator, hypocenter | C257 | C32 |
| Fitting | C16×C257 | C2 |
| socle | C2×C257 | C16 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C16 | |
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^2562080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D257, C2×#22551498, #30656570, … |
| maximal normal subgroup of | C32×D257, C2×#22551498, #30656570, … |
| maximal quotient of | #30656456, C2×#22551498 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 52);