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C2×C3×C5⋊D35 #14523678

order2100
isoclinismisoclinic class of C5⋊D35
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3×C5⋊D35
unambiguous semidirect product(C2×C5)⋊(C3×D35)

Splittings

Fitting, socleC2×C3×C52×C7 ⋊ C2
derived, HallC52×C7 ⋊ C22×C3
HallC3×C52×C7 ⋊ C22
HallC3×C52 ⋊ C2×D7
SylowC52 ⋊ C2×C3×D7
HallC3×C7 ⋊ C2×C5⋊D5
SylowC7 ⋊ C2×C3×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊D35
commutator, cosocle, hypocenterC52×C7C22×C3
FrattiniC1G
Fitting, socleC2×C3×C52×C7C2
LCSG ▷ C52×C7
UCSC1 ◁ C2×C3

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1050

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C3×C5⋊D245, AGL(1,𝔽7)×C5⋊D35, C2×C5⋊(C5⋊(ΓL(1,𝔽8)⋊D7)), …
maximal normal subgroup ofC2×C3×C7×C5⋊D35, C2×C3×C11×C5⋊D35, C2×C3×C13×C5⋊D35, …
maximal quotient ofC2×C3×C5⋊D245, AGL(1,𝔽7)×C5⋊D35, C2×C5⋊(C5⋊(ΓL(1,𝔽8)⋊D7)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 158);