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C2×C3×C7×C5⋊D5 #14523677

order2100
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3×C7×C5⋊D5
unambiguous semidirect product(C2×C5)⋊(C3×C7×D5)

Splittings

Fitting, socleC2×C3×C52×C7 ⋊ C2
derived, SylowC52 ⋊ C22×C3×C7
HallC3×C52×C7 ⋊ C22
HallC52×C7 ⋊ C22×C3
HallC3×C52 ⋊ C22×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C5⋊D5
commutator, cosocle, hypocenterC52C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C7C2
LCSG ▷ C52
UCSC1 ◁ C2×C3×C7

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1050

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×C49×C5⋊D5, C7×AGL(1,𝔽7)×C5⋊D5, C2×C7×C5⋊(C5⋊AGL(1,𝔽7)), …
maximal normal subgroup ofC2×C3×C49×C5⋊D5, C2×C3×C72×C5⋊D5, C2×C3×C7×C11×C5⋊D5, …
maximal quotient ofC2×C3×C49×C5⋊D5, C7×AGL(1,𝔽7)×C5⋊D5, C2×C7×C5⋊(C5⋊AGL(1,𝔽7)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 157);