Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C197 ⋊ C2 |
| Sylow | C197 ⋊ #104 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22⋊D197 |
| commutator | C4×C197 | C2×C4 |
| Frattini | C2×C4 | C2×D197 |
| Fitting | M16×C197 | C2 |
| socle | C2×C197 | C22⋊C4 |
| hypercenter | M16 | D197 |
| hypocenter | C197 | #104 |
| LCS | G ▷ C4×C197 ▷ C2×C197 ▷ C197 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ M16 | |
44 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,197|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,c^b=ce,f^b=f^196994 conjugacy classes — view the full character table.
| maximal subgroup of | #104×D197, C2×#20263252, #27161094, … |
| maximal normal subgroup of | #104×D197, C2×#20263252, #27161094, … |
| maximal quotient of | #27160806, #27160809, #27160814, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 72);