Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q32×C97 ⋊ C2 |
| Sylow | C97 ⋊ SD64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15690751 |
| commutator | C16×C97 | C22 |
| Frattini | C16 | C2×D97 |
| Fitting | Q32×C97 | C2 |
| socle | C2×C97 | D16 |
| hypercenter | Q32 | D97 |
| hypocenter | C97 | SD64 |
| LCS | G ▷ C16×C97 ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q32 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,c^b=cd,d^b=de,e^b=ef,g^b=g^96547 conjugacy classes — view the full character table.
| maximal subgroup of | SD64×D97, C2×#20260572, #27144043, … |
| maximal normal subgroup of | SD64×D97, C2×#20260572, #27144043, … |
| maximal quotient of | #27139913, #27139917, #27139937, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 386);