Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C97 ⋊ #331 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊Dic97 |
| commutator | C2×C4×C97 | C2×C4 |
| Frattini | C42 | C2×D97 |
| Fitting | #127×C97 | C2 |
| socle | C22×C97 | C22⋊C4 |
| hypercenter | #127 | D97 |
| hypocenter | C97 | #331 |
| LCS | G ▷ C2×C4×C97 ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #127 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,c^2=f,d^2=ef,b^a=bc,c^a=ce,g^a=g^96,c^b=cf,d^b=def691 conjugacy classes — view the full character table.
| maximal subgroup of | #27139880, #27139881, #331×D97, … |
| maximal normal subgroup of | #27139880, #27139881, #331×D97, … |
| maximal quotient of | #27139557, #27139619, #27139773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 293);