Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C97 ⋊ #344 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13095488 |
| commutator | C22×C97 | C42 |
| Frattini | C22×C4 | C2×D97 |
| Fitting | C2×M16×C97 | C2 |
| socle | C2×C97 | #95 |
| hypercenter | C2×M16 | D97 |
| hypocenter | C97 | #344 |
| LCS | G ▷ C22×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C2×M16 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,b^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^96,d^b=df,g^b=g^96982 conjugacy classes — view the full character table.
| maximal subgroup of | #344×D97, C2×#20260507, #27141537, … |
| maximal normal subgroup of | #344×D97, C2×#20260507, #27141537, … |
| maximal quotient of | #27139580, #27139582, #27139587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 321);