Finite Group DatabasebetaFinite Group Databasebeta| order | 6304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#13096802 |
| Sylow | C197 ⋊ C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D197 |
| commutator | C2×C197 | C2×C8 |
| Fitting | C42×C197 | C2 |
| socle | C22×C197 | C2×C4 |
| hypercenter | C42 | D197 |
| hypocenter | C197 | C4⋊C8 |
| LCS | G ▷ C2×C197 ▷ C197 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,197|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^1961588 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊#13096802, #27160808, Q8⋊#13096802, … |
| maximal normal subgroup of | D4⋊#13096802, #27160808, Q8⋊#13096802, … |
| maximal quotient of | #27160830, #27160832, #27160834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6304, 76);