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C2×C5×D105 #14523682

order2100
isoclinismisoclinic class of D105
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D105
unambiguous semidirect product(C2×C3)⋊(C5×D35)
unambiguous semidirect product(C2×C5)⋊(C5×D21)
unambiguous semidirect product(C2×C7)⋊(C5×D15)

Splittings

Fitting, socleC2×C3×C52×C7 ⋊ C2
derivedC3×C5×C7 ⋊ C22×C5
HallC3×C52×C7 ⋊ C22
HallC52×C7 ⋊ C2×D3
HallC3×C52 ⋊ C2×D7
SylowC52 ⋊ C2×D21
HallC3×C7 ⋊ C2×C5×D5
SylowC7 ⋊ C2×C5×D15
SylowC3 ⋊ C2×C5×D35

Subgroups

subgroupG/H
center, hypercenterC2×C5D105
commutator, cosocle, hypocenterC3×C5×C7C22×C5
FrattiniC1G
Fitting, socleC2×C3×C52×C7C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 420

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C5×D735, C5×D7×D105, C2×C5×C3⋊(C5⋊(C7⋊D7)), …
maximal normal subgroup ofC2×C5×C7×D105, C2×C5×C11×D105, C2×C5×C13×D105, …
maximal quotient ofC2×C5×D735, C5×D7×D105, C2×C5×C3⋊(C5⋊(C7⋊D7)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 162);