Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C197 ⋊ C2 |
| Sylow | C197 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D197 |
| commutator, socle | C2×C197 | C22×C4 |
| Fitting | M16×C197 | C2 |
| hypercenter | M16 | D197 |
| hypocenter | C197 | #131 |
| LCS | G ▷ C2×C197 ▷ C197 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,197|a^2=d,d^2=e,f^a=f^196,c^b=ce,f^c=f^1961000 conjugacy classes — view the full character table.
| maximal subgroup of | #27161193, #27161195, #27161198, … |
| maximal normal subgroup of | #27161193, #27161195, #27161198, … |
| maximal quotient of | #27161036, #27161037, #27161044, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 154);