Finite Group DatabasebetaFinite Group Databasebeta| order | 7100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊(D71⋊C5) |
| unambiguous semidirect product | (C2×C5)⋊(D71⋊C5) |
| unambiguous semidirect product | (C2×C71⋊C5)⋊D5 |
| unambiguous semidirect product | (C2×D355)⋊C5 |
| Fitting, socle | C2×C5×C71 ⋊ C2×C5 |
| derived | C5×C71 ⋊ C22×C5 |
| Hall | C5×C71⋊C5 ⋊ C22 |
| Sylow | C71 ⋊ C2×C5×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊(D71⋊C5) |
| commutator, hypocenter | C5×C71 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C71 | C2×C5 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
110 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C5⋊(D71⋊C5), C2×C3×C5⋊(D71⋊C5), C2×C3⋊(C5⋊(D71⋊C5)) |
| maximal normal subgroup of | C2×C3×C5⋊(D71⋊C5) |
| maximal quotient of | D3×C5⋊(D71⋊C5), C2×C3×C5⋊(D71⋊C5), C2×C3⋊(C5⋊(D71⋊C5)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7100, 31);