Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C97 ⋊ #322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×#87604 |
| commutator | C2×C97 | C4×C8 |
| Fitting | C2×C8×C97 | C4 |
| socle | C22×C97 | C42 |
| hypercenter | C2×C8 | #87604 |
| hypocenter | C97 | #322 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^b=g^22,g^d=g^96424 conjugacy classes — view the full character table.
| maximal subgroup of | #27156652, #27156653, #27156655, … |
| maximal normal subgroup of | #27156652, #27156653, #27156655, … |
| maximal quotient of | #27156558, #27156649, #27156651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1390);