Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C197 ⋊ C2 |
| Sylow | C197 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D197 |
| commutator, socle | C2×C197 | C24 |
| Fitting | C2×D4×C197 | C2 |
| hypercenter | C2×D4 | D197 |
| hypocenter | C197 | H(5,𝔽2) |
| LCS | G ▷ C2×C197 ▷ C197 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,197|b^a=be,d^a=de,c^b=ce,f^d=f^196997 conjugacy classes — view the full character table.
| maximal subgroup of | #27161246, #27161249, #27161256, … |
| maximal normal subgroup of | #27161246, #27161249, #27161256, … |
| maximal quotient of | #27161551, #27161552, #27161554, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 191);