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D3×C7×C71⋊C5 #28415869

order14910
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productD3×C7×C71⋊C5
unambiguous semidirect productC3⋊(C2×C7×C71⋊C5)
unambiguous semidirect product(D3×C7×C71)⋊C5

Splittings

Fitting, socle, HallC3×C7×C71 ⋊ C2×C5
derived, HallC3×C71 ⋊ C2×C5×C7
HallC3×C7×C71⋊C5 ⋊ C2
HallD3×C7×C71 ⋊ C5
HallC3×C71⋊C5 ⋊ C2×C7
HallC7×C71 ⋊ C5×D3
HallD3×C71 ⋊ C5×C7
SylowC71 ⋊ C5×D3×C7
HallC3×C7 ⋊ C2×C71⋊C5
SylowC3 ⋊ C2×C7×C71⋊C5

Subgroups

subgroupG/H
center, hypercenterC7D3×C71⋊C5
commutator, cosocle, hypocenterC3×C71C2×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C71C2×C5
LCSG ▷ C3×C71
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1491

Conjugacy classes & character table

399 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C7×D71⋊C5, D3×C7⋊(D71⋊C5), D3×D7×C71⋊C5, …
maximal normal subgroup ofD3×C7×D71⋊C5, D3×C7⋊(D71⋊C5), D3×D7×C71⋊C5, …
maximal quotient ofC7×Dic3×C71⋊C5, C2×D3×C7×C71⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 32);