Finite Group Databasebeta

← Prev (#28415870) Next (#28415872) →

D21×C71⋊C5 #28415871

order14910
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD21×C71⋊C5
unambiguous semidirect productC3⋊(D7×C71⋊C5)
unambiguous semidirect productC7⋊(D3×C71⋊C5)
unambiguous semidirect product(D21×C71)⋊C5

Splittings

Fitting, socle, derived, HallC3×C7×C71 ⋊ C2×C5
HallC3×C7×C71⋊C5 ⋊ C2
HallD21×C71 ⋊ C5
HallC7×C71⋊C5 ⋊ D3
HallC3×C71⋊C5 ⋊ D7
HallC7×C71 ⋊ C5×D3
HallC3×C71 ⋊ C5×D7
SylowC71 ⋊ C5×D21
HallC3×C7 ⋊ C2×C71⋊C5
SylowC7 ⋊ D3×C71⋊C5
SylowC3 ⋊ D7×C71⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C71C2×C5
LCSG ▷ C3×C7×C71
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1491

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD21×D71⋊C5, D21⋊(D71⋊C5), D3×D7×C71⋊C5, …
maximal normal subgroup ofD21×D71⋊C5, D21⋊(D71⋊C5), D3×D7×C71⋊C5, …
maximal quotient ofDic21×C71⋊C5, C2×D21×C71⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 34);