Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C197 ⋊ C2 |
| Sylow | C197 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D197 |
| commutator, socle | C22×C197 | C23 |
| Fitting | C22⋊C4×C197 | C2 |
| hypercenter | C22⋊C4 | D197 |
| hypocenter | C197 | #121 |
| LCS | G ▷ C22×C197 ▷ C197 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,197|b^2=d,b^a=bd,c^a=ce,f^b=f^196,f^c=f^196994 conjugacy classes — view the full character table.
| maximal subgroup of | #121×D197, C2×#20263299, #27161587, … |
| maximal normal subgroup of | #121×D197, C2×#20263299, #27161587, … |
| maximal quotient of | #27160938, #27160955, #27160957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 119);