Finite Group DatabasebetaFinite Group Databasebeta| order | 6100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×D61⋊C25 |
| unambiguous semidirect product | D61⋊(C2×C25) |
| unambiguous semidirect product | (C2×D61)⋊C25 |
| unambiguous semidirect product | (C61⋊C25)⋊C22 |
| unambiguous semidirect product | (C2×C61⋊C25)⋊C2 |
| derived, Sylow | C61 ⋊ C22×C25 |
| Hall | C61⋊C25 ⋊ C22 |
| Hall | C2×D61 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D61⋊C5 |
| commutator, hypocenter | C61 | C22×C25 |
| Frattini | C5 | C2×D61⋊C5 |
| Fitting, socle | C2×C5×C61 | C2×C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C5 | |
30 conjugacy classes of subgroups.
160 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(D61⋊C3)⋊C25, D3×D61⋊C25, C2×C3×D61⋊C25, … |
| maximal normal subgroup of | C2×(D61⋊C3)⋊C25, C2×C3×D61⋊C25 |
| maximal quotient of | D3×D61⋊C25, C2×C3×D61⋊C25, C2×C3⋊(D61⋊C25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6100, 9);