Finite Group DatabasebetaFinite Group Databasebeta| order | 6208 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C97 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #13095525 |
| commutator, hypocenter | C97 | C64 |
| Fitting | C4×C97 | C16 |
| socle | C2×C97 | C32 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C4 | |
14 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,97|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^8,g^b=g^64,g^c=g^22,g^d=g^9688 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20261859, #27159018, #27159019, … |
| maximal normal subgroup of | C2×#20261859, #27159018, #27159019, … |
| maximal quotient of | #27158993, C2×#20261859 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6208, 1673);