Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C97 ⋊ C2 |
| Sylow | C97 ⋊ #510 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D8×D97 |
| commutator | C8×C97 | C23 |
| Frattini | C8 | C22×D97 |
| Fitting | Q32×C97 | C2 |
| socle | C2×C97 | C2×D8 |
| hypercenter | Q32 | D97 |
| hypocenter | C97 | #510 |
| LCS | G ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32 | |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|b^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^96,d^b=de,e^b=ef,g^c=g^96544 conjugacy classes — view the full character table.
| maximal subgroup of | #510×D97, C2×#20261177, #27154869, … |
| maximal normal subgroup of | #510×D97, C2×#20261177, #27154869, … |
| maximal quotient of | #27143447, #27143454, #27143521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 991);