Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C257 ⋊ #101 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,257|a^2=d,b^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^241,d^b=de,f^d=f^256523 conjugacy classes — view the full character table.
| maximal subgroup of | #30657645, #30657646, #30657647, … |
| maximal normal subgroup of | #30657645, #30657646, #30657647, … |
| maximal quotient of | #30657582, #30657583, #30657594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 207);