Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C16×C97 ⋊ C4 |
| Sylow | C97 ⋊ #366 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15690879 |
| commutator | C8×C97 | C2×C4 |
| Frattini | C8 | C2×#87604 |
| Fitting | C16×C97 | C4 |
| socle | C2×C97 | #107 |
| hypercenter | C16 | #87604 |
| hypocenter | C97 | #366 |
| LCS | G ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,b^2=ce,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^22,g^d=g^96406 conjugacy classes — view the full character table.
| maximal subgroup of | #27156885, #27156886, #27156897, … |
| maximal normal subgroup of | #27156885, #27156886, #27156897, … |
| maximal quotient of | #27156767, #27156768, #27156794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1475);