Finite Group DatabasebetaFinite Group Databasebeta| order | 7228 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C139 · Schur multiplier (H2) = C1 |
| direct product | #261×C139 |
| Fitting, socle, Hall | C13×C139 ⋊ C4 |
| derived, Sylow | C13 ⋊ C4×C139 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C139 | #261 |
| commutator, hypocenter | C13 | C4×C139 |
| Frattini | C1 | G |
| Fitting, socle | C13×C139 | C4 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C139 | |
12 conjugacy classes of subgroups.
973 conjugacy classes — view the full character table.
| maximal subgroup of | C139×AGL(1,𝔽13), #36343627, #36343628, … |
| maximal normal subgroup of | C139×AGL(1,𝔽13), #36343627, #36343628, … |
| maximal quotient of | C3×#261×C139, C139×C3⋊#261, C5×#261×C139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7228, 6);