Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C197 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D197 |
| commutator | C2×C197 | C22×C4 |
| Fitting | C22⋊C4×C197 | C2 |
| socle | C22×C197 | C23 |
| hypercenter | C22⋊C4 | D197 |
| hypocenter | C197 | #117 |
| LCS | G ▷ C2×C197 ▷ C197 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,197|a^2=e,c^2=d,b^a=bd,f^c=f^1961000 conjugacy classes — view the full character table.
| maximal subgroup of | #27161051, #117×D197, C2×#20263282, … |
| maximal normal subgroup of | #27161051, #117×D197, C2×#20263282, … |
| maximal quotient of | #27160924, C22⋊C4×Dic197, #27160930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 102);