Finite Group DatabasebetaFinite Group Databasebeta| order | 5004 |
| isoclinism | isoclinic class of D139 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×D139 |
| Fitting | C2×C9×C139 ⋊ C2 |
| derived, Sylow | C139 ⋊ C22×C9 |
| Hall | C9×C139 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D139 |
| commutator, hypocenter | C139 | C22×C9 |
| Frattini | C3 | C2×C3×D139 |
| Fitting | C2×C9×C139 | C2 |
| socle | C2×C3×C139 | C2×C3 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C9 | |
30 conjugacy classes of subgroups.
1278 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D5×D139, C2×C9×D695, C2×C5×C9×D139, … |
| maximal normal subgroup of | C2×C5×C9×D139, C2×C7×C9×D139 |
| maximal quotient of | C9×D5×D139, C2×C9×D695, C2×C5×C9×D139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5004, 13);