Finite Group DatabasebetaFinite Group Databasebeta| order | 5980 |
| isoclinism | isoclinic class of D115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×D115 |
| unambiguous semidirect product | (C2×C5)⋊(C13×D23) |
| unambiguous semidirect product | (C2×C23)⋊(D5×C13) |
| Fitting, socle | C2×C5×C13×C23 ⋊ C2 |
| derived, Hall | C5×C23 ⋊ C22×C13 |
| Hall | C5×C13×C23 ⋊ C22 |
| Hall | C13×C23 ⋊ C2×D5 |
| Hall | C5×C13 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D5×C13 |
| Sylow | C5 ⋊ C2×C13×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D115 |
| commutator, hypocenter | C5×C23 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C13×C23 | C2 |
| LCS | G ▷ C5×C23 | |
| UCS | C1 ◁ C2×C13 | |
40 conjugacy classes of subgroups.
1534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C13⋊C3×D115, D3×C13×D115, C2×C13×D345, … |
| maximal normal subgroup of | C2×C13⋊C3×D115, C2×C3×C13×D115, C2×C5×C13×D115 |
| maximal quotient of | D3×C13×D115, C2×C13×D345, C2×C3×C13×D115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5980, 31);