Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C97 ⋊ #473 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15690782 |
| commutator | C2×C4×C97 | C23 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #137×C97 | C2 |
| socle | C2×C97 | #121 |
| hypercenter | #137 | D97 |
| hypocenter | C97 | #473 |
| LCS | G ▷ C2×C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #137 | |
100 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,97|a^2=f,b^2=df,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^b=g^96,e^c=ef544 conjugacy classes — view the full character table.
| maximal subgroup of | #473×D97, C2×#20261008, #27151451, … |
| maximal normal subgroup of | #473×D97, C2×#20261008, #27151451, … |
| maximal quotient of | #27141099, #27141104, #27141123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 822);