Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#13095525 |
| unambiguous semidirect product | (C2×#13095525)⋊C2 |
| Fitting | C22×C97 ⋊ C16 |
| Sylow | C97 ⋊ C22⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#13095525 |
| commutator, socle | C2×C97 | C2×C16 |
| Fitting | C22×C97 | C16 |
| hypercenter | C22 | #13095525 |
| hypocenter | C97 | C22⋊C16 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C22 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,d^2=e,e^2=f,b^a=bc,g^a=g^8,g^d=g^64,g^e=g^22,g^f=g^9664 conjugacy classes — view the full character table.
| maximal subgroup of | #27158996, #27158997, C2×C22⋊#13095525, … |
| maximal normal subgroup of | #27158996, #27158997, C2×C22⋊#13095525, … |
| maximal quotient of | #27158996, #27158997, D4⋊#13095525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1675);