Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C97 ⋊ #349 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊Dic97 |
| commutator | C22×C97 | C2×C8 |
| Frattini | C2×C8 | C2×D97 |
| Fitting | C2×M16×C97 | C2 |
| socle | C2×C97 | C22⋊C8 |
| hypercenter | C2×M16 | D97 |
| hypocenter | C97 | #349 |
| LCS | G ▷ C22×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ C2×M16 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^96,d^b=df982 conjugacy classes — view the full character table.
| maximal subgroup of | #27139671, #27139672, #27139673, … |
| maximal normal subgroup of | #27139671, #27139672, #27139673, … |
| maximal quotient of | #27139660, #27139676, #27139694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 331);