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D3×(C71⋊C5)⋊C7 #28415874

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

Aliases

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

Splittings

Fitting, socle, derived, HallC3×C71 ⋊ C2×C5×C7
HallC3×(C71⋊C5)⋊C7 ⋊ C2
HallD3×C71⋊C7 ⋊ C5
HallD3×C71⋊C5 ⋊ C7
HallC3×C71⋊C7 ⋊ C2×C5
HallC3×C71⋊C5 ⋊ C2×C7
HallC71⋊C7 ⋊ C5×D3
HallD3×C71 ⋊ C5×C7
HallC71⋊C5 ⋊ D3×C7
SylowC71 ⋊ C5×D3×C7
SylowC3 ⋊ C2×(C71⋊C5)⋊C7

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 213

Conjugacy classes & character table

111 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽71), C2×D3×(C71⋊C5)⋊C7
maximal normal subgroup ofD3×AGL(1,𝔽71), C2×D3×(C71⋊C5)⋊C7
maximal quotient ofDic3×(C71⋊C5)⋊C7, C2×D3×(C71⋊C5)⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 37);