Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C97 ⋊ #346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#11715906 |
| commutator, socle | C2×C97 | C4×C8 |
| Fitting | C8×C97 | C8 |
| hypercenter | C8 | #11715906 |
| hypocenter | C97 | #346 |
| LCS | G ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C8 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^a=g^64,g^b=g^75,g^c=g^22,g^d=g^96,g^e=g^96136 conjugacy classes — view the full character table.
| maximal subgroup of | #27158755, #27158756, #27158784, … |
| maximal normal subgroup of | #27158755, #27158756, #27158784, … |
| maximal quotient of | #27158752, #27158753, #27158807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1644);