Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11715895 |
| Sylow | C97 ⋊ Q8⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22⋊D97 |
| commutator | C4×C97 | C2×C8 |
| Frattini | C42 | C2×D97 |
| Fitting | C4×Q8×C97 | C2 |
| socle | C22×C97 | C22⋊C4 |
| hypercenter | C4×Q8 | D97 |
| hypocenter | C97 | Q8⋊C8 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ C4×Q8 | |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^96,c^b=ce988 conjugacy classes — view the full character table.
| maximal subgroup of | Q8⋊C8×D97, C2×Q8⋊#11715895, #27140117, … |
| maximal normal subgroup of | Q8⋊C8×D97, C2×Q8⋊#11715895, #27140117, … |
| maximal quotient of | #27139559, #27139562, #27139577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 280);