Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D8×C197 ⋊ C2 |
| Sylow | C197 ⋊ D16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15691343 |
| commutator | C8×C197 | C22 |
| Frattini | C8 | C2×D197 |
| Fitting | D8×C197 | C2 |
| socle | C2×C197 | D8 |
| hypercenter | D8 | D197 |
| hypocenter | C197 | D16 |
| LCS | G ▷ C8×C197 ▷ C4×C197 ▷ C2×C197 ▷ C197 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D8 | |
28 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,197|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^196697 conjugacy classes — view the full character table.
| maximal subgroup of | D16×D197, C2×#20263267, #27161509, … |
| maximal normal subgroup of | D16×D197, C2×#20263267, #27161509, … |
| maximal quotient of | #27160879, #27160880, #27160904, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 87);