Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #97×C97 ⋊ C2 |
| Sylow | C97 ⋊ #329 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #13095488 |
| commutator | C2×C4×C97 | C2×C4 |
| Frattini | C42 | C2×D97 |
| Fitting | #97×C97 | C2 |
| socle | C22×C97 | C22⋊C4 |
| hypercenter | #97 | D97 |
| hypocenter | C97 | #329 |
| LCS | G ▷ C2×C4×C97 ▷ C22×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,c^2=f,d^2=e,b^a=bc,c^a=ce,c^b=cf,d^b=def,g^b=g^96979 conjugacy classes — view the full character table.
| maximal subgroup of | #329×D97, C2×#20260474, #27140322, … |
| maximal normal subgroup of | #329×D97, C2×#20260474, #27140322, … |
| maximal quotient of | #27139556, #27139561, #27139618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 288);