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C3×C7⋊(D71⋊C5) #28415868

order14910
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊(D71⋊C5)
unambiguous semidirect product(C71⋊C5)⋊(C3×D7)
unambiguous semidirect product(C3×D497)⋊C5

Splittings

Fitting, socle, HallC3×C7×C71 ⋊ C2×C5
derived, HallC7×C71 ⋊ C2×C3×C5
HallC3×C7×C71⋊C5 ⋊ C2
HallC3×D497 ⋊ C5
HallC7×C71⋊C5 ⋊ C2×C3
HallC3×C71⋊C5 ⋊ D7
HallD497 ⋊ C3×C5
HallC71⋊C5 ⋊ C3×D7
HallC3×C71 ⋊ C5×D7
SylowC71 ⋊ C3×C5×D7
HallC3×C7 ⋊ D71⋊C5
SylowC7 ⋊ C3×D71⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(D71⋊C5)
commutator, cosocle, hypocenterC7×C71C2×C3×C5
FrattiniC1G
Fitting, socleC3×C7×C71C2×C5
LCSG ▷ C7×C71
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1491

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D7×D71⋊C5, D3×C7⋊(D71⋊C5), D21⋊(D71⋊C5), …
maximal normal subgroup ofC3×D7×D71⋊C5, D3×C7⋊(D71⋊C5), D21⋊(D71⋊C5), …
maximal quotient ofC3×C7⋊(Dic71⋊C5), C2×C3×C7⋊(D71⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 31);