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D7×C3⋊(C5⋊D5) #14523655

order2100
isoclinismisoclinic class of D7×C3⋊(C5⋊D5)
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C5

Aliases

direct productD7×C3⋊(C5⋊D5)
unambiguous semidirect product(C3×D7)⋊(C5⋊D5)
unambiguous semidirect product(C5×D7)⋊D15

Splittings

Fitting, socle, derived, HallC3×C52×C7 ⋊ C22
HallC52×C7 ⋊ C2×D3
HallC3×C52 ⋊ C2×D7
SylowC52 ⋊ D3×D7
HallC3×C7 ⋊ C2×C5⋊D5
SylowC7 ⋊ C2×C3⋊(C5⋊D5)
SylowC3 ⋊ D7×C5⋊D5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7C22
LCSG ▷ C3×C52×C7
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 525

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD49×C3⋊(C5⋊D5), C7×D7×C3⋊(C5⋊D5), C7⋊D7×C3⋊(C5⋊D5), …
maximal normal subgroup ofC7×D7×C3⋊(C5⋊D5), C11×D7×C3⋊(C5⋊D5), C13×D7×C3⋊(C5⋊D5), …
maximal quotient ofD49×C3⋊(C5⋊D5), C7×D7×C3⋊(C5⋊D5), C7⋊D7×C3⋊(C5⋊D5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 135);