Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C97 ⋊ Q8⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22⋊D97 |
| commutator | C4×C97 | C2×C8 |
| Frattini | C42 | C2×D97 |
| Fitting | C4⋊C8×C97 | C2 |
| socle | C22×C97 | C22⋊C4 |
| hypercenter | C4⋊C8 | D97 |
| hypocenter | C97 | Q8⋊C8 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8 | |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,c^b=ce,g^b=g^96988 conjugacy classes — view the full character table.
| maximal subgroup of | Q8⋊C8×D97, C2×#20260465, #27140115, … |
| maximal normal subgroup of | Q8⋊C8×D97, C2×#20260465, #27140115, … |
| maximal quotient of | #27139558, #27139561, #27139575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 279);