Finite Group DatabasebetaFinite Group Databasebeta| order | 6100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D5×C61⋊C5 |
| unambiguous semidirect product | C5⋊(C22×C61⋊C5) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C61⋊C5) |
| unambiguous semidirect product | (C2×D5×C61)⋊C5 |
| Fitting, socle | C2×C5×C61 ⋊ C2×C5 |
| derived | C5×C61 ⋊ C22×C5 |
| Hall | C5×C61⋊C5 ⋊ C22 |
| Sylow | C61 ⋊ C2×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×C61⋊C5 |
| commutator, hypocenter | C5×C61 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C61 | C2×C5 |
| LCS | G ▷ C5×C61 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
136 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D5×(C61⋊C3)⋊C5, D3×D5×C61⋊C5, C2×C3×D5×C61⋊C5, … |
| maximal normal subgroup of | C2×D5×(C61⋊C3)⋊C5, C2×C3×D5×C61⋊C5 |
| maximal quotient of | D3×D5×C61⋊C5, C2×C3×D5×C61⋊C5, C2×D15×C61⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6100, 41);