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C2×C7×C3⋊(C5⋊D5) #14523683

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

Aliases

direct productC2×C7×C3⋊(C5⋊D5)
unambiguous semidirect product(C2×C3)⋊(C7×C5⋊D5)
unambiguous semidirect product(C2×C5)⋊(C7×D15)

Splittings

Fitting, socleC2×C3×C52×C7 ⋊ C2
derived, HallC3×C52 ⋊ C22×C7
HallC3×C52×C7 ⋊ C22
HallC52×C7 ⋊ C2×D3
SylowC52 ⋊ C2×D3×C7
HallC3×C7 ⋊ C2×C5⋊D5
SylowC3 ⋊ C2×C7×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52C22×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C7C2
LCSG ▷ C3×C52
UCSC1 ◁ C2×C7

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1050

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC2×C49×C3⋊(C5⋊D5), C7×D7×C3⋊(C5⋊D5), C2×C7×C3⋊(C5⋊D35), …
maximal normal subgroup ofC2×C49×C3⋊(C5⋊D5), C2×C72×C3⋊(C5⋊D5), C2×C7×C11×C3⋊(C5⋊D5), …
maximal quotient ofC2×C49×C3⋊(C5⋊D5), C7×D7×C3⋊(C5⋊D5), C2×C7×C3⋊(C5⋊D35), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 163);