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C3×D7×C71⋊C5 #28415867

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

Aliases

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

Splittings

Fitting, socle, HallC3×C7×C71 ⋊ C2×C5
derived, HallC7×C71 ⋊ C2×C3×C5
HallC3×C7×C71⋊C5 ⋊ C2
HallC3×D7×C71 ⋊ C5
HallC7×C71⋊C5 ⋊ C2×C3
HallD7×C71 ⋊ C3×C5
HallC3×C71 ⋊ C5×D7
SylowC71 ⋊ C3×C5×D7
HallC3×C7 ⋊ C2×C71⋊C5
SylowC7 ⋊ C2×C3×C71⋊C5

Subgroups

subgroupG/H
center, hypercenterC3D7×C71⋊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

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

Relationships

maximal subgroup ofC3×D7×D71⋊C5, D7×C3⋊(D71⋊C5), D3×D7×C71⋊C5, …
maximal normal subgroup ofC3×D7×D71⋊C5, D7×C3⋊(D71⋊C5), D3×D7×C71⋊C5, …
maximal quotient ofC3×Dic7×C71⋊C5, C2×C3×D7×C71⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 30);