Finite Group DatabasebetaFinite Group Databasebeta| order | 5054 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C192 · Schur multiplier (H2) = C19 |
| direct product | D7×C192 |
| unambiguous semidirect product | C7⋊(C2×C192) |
| Fitting, socle, Hall | C7×C192 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C192 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C192 | D7 |
| commutator, hypocenter | C7 | C2×C192 |
| Frattini | C1 | G |
| Fitting, socle | C7×C192 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C192 | |
88 conjugacy classes of subgroups.
1805 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C192×AGL(1,𝔽7), C19×#11716325, C19×#11716326, … |
| maximal normal subgroup of | C192×AGL(1,𝔽7), C19×#11716325, C19×#11716326, … |
| maximal quotient of | C192×D21, C3×D7×C192, C5×D7×C192, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5054, 8);