Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #102×C97 ⋊ C2 |
| Sylow | C97 ⋊ #450 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D97 |
| commutator | C2×C4×C97 | C23 |
| Frattini | C2×C4 | C22×D97 |
| Fitting | #102×C97 | C2 |
| socle | C22×C97 | C2×D4 |
| hypercenter | #102 | D97 |
| hypocenter | C97 | #450 |
| LCS | G ▷ C2×C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ #102 | |
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 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,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^96,d^b=df,g^c=g^96691 conjugacy classes — view the full character table.
| maximal subgroup of | #450×D97, C2×#20260887, #27150951, … |
| maximal normal subgroup of | #450×D97, C2×#20260887, #27150951, … |
| maximal quotient of | #27140689, #27140706, #27140757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 701);