Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C97 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #13095525 |
| commutator, hypocenter | C97 | C2×C32 |
| Frattini | C2 | C2×#13095525 |
| Fitting | C4×C97 | C16 |
| socle | C2×C97 | C2×C16 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C4 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^8,g^b=g^96,g^c=g^64,g^d=g^22,g^e=g^9688 conjugacy classes — view the full character table.
| maximal subgroup of | #27159004, #27159006, #27159011, … |
| maximal normal subgroup of | #27159004, #27159006, #27159011, … |
| maximal quotient of | C4×#15690909, #27159008, #27159014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1678);