Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #124×C97 ⋊ C2 |
| Sylow | C97 ⋊ #496 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×C22⋊D97 |
| commutator | C2×C4×C97 | C23 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #124×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | #124 | D97 |
| hypocenter | C97 | #496 |
| LCS | G ▷ C2×C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #124 | |
144 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^96,c^b=cf,g^b=g^96688 conjugacy classes — view the full character table.
| maximal subgroup of | #27139892, #27139894, #27141025, … |
| maximal normal subgroup of | #27139892, #27139894, #27141025, … |
| maximal quotient of | #27141360, #27141366, #27141377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 939);