Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C97 ⋊ H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×Dic97 |
| commutator | C4×C97 | C42 |
| Frattini | C22×C4 | C2×D97 |
| Fitting | #117×C97 | C2 |
| socle | C2×C97 | #95 |
| hypercenter | #117 | D97 |
| hypocenter | C97 | H(3,ℤ/4) |
| LCS | G ▷ C4×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ #117 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,b^2=e,c^2=f,b^a=bc,e^a=ef,d^b=df,g^b=g^96982 conjugacy classes — view the full character table.
| maximal subgroup of | H(3,ℤ/4)×D97, C2×#20260491, #27141490, … |
| maximal normal subgroup of | H(3,ℤ/4)×D97, C2×#20260491, #27141490, … |
| maximal quotient of | #27139564, #27139565, #27139566, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 305);