Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C49⋊#6157 |
| Fitting, derived, Hall | C49×C53 ⋊ C4 |
| Sylow | C53 ⋊ Dic49 |
| Sylow | C49 ⋊ #6157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C49×C53 | C4 |
| Frattini | C7 | C7⋊#6157 |
| socle | C7×C53 | Dic7 |
| prime radical | C7×D53 | D7 |
| cosocle | C49×D53 | C2 |
| LCS | G ▷ C49×C53 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,53,7|a^2=b,c^7=e^6,c^a=c^6e,d^a=d^30,e^a=e^6,d^b=d^52689 conjugacy classes — view the full character table.
| maximal subgroup of | (C49⋊C3)⋊#6157, C3×C49⋊#6157, C3⋊(C49⋊#6157) |
| maximal normal subgroup of | (C49⋊C3)⋊#6157, C3×C49⋊#6157 |
| maximal quotient of | C3×C49⋊#6157, C3⋊(C49⋊#6157) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 7);