Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#13095514 |
| Sylow | C97 ⋊ C22⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×#87604 |
| commutator | C2×C97 | C2×C16 |
| Fitting | C22×C4×C97 | C4 |
| socle | C22×C97 | C2×C8 |
| hypercenter | C22×C4 | #87604 |
| hypocenter | C97 | C22⋊C16 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
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^22,g^d=g^96424 conjugacy classes — view the full character table.
| maximal subgroup of | #27156656, #27156657, #27156658, … |
| maximal normal subgroup of | #27156656, #27156657, #27156658, … |
| maximal quotient of | #27156656, #27156672, D4⋊#13095514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1443);