Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C197 ⋊ C2 |
| Sylow | C197 ⋊ SD32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D1576 |
| commutator | C8×C197 | C22 |
| Frattini | C8 | C2×D197 |
| Fitting | C16×C197 | C2 |
| socle | C2×C197 | D8 |
| hypercenter | C16 | D197 |
| hypocenter | C197 | SD32 |
| LCS | G ▷ C8×C197 ▷ C4×C197 ▷ C2×C197 ▷ C197 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,197|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^196,c^b=cd,d^b=de,f^b=f^1961579 conjugacy classes. The character table is too large to display.
| maximal subgroup of | SD32×D197, C2×#20263271, #27161510, … |
| maximal normal subgroup of | SD32×D197, C2×#20263271, #27161510, … |
| maximal quotient of | #27160881, #27160884, #27160907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 91);