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C2×C5×D5×D7 #13063854

order1400
isoclinismisoclinic class of D5×D7
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C5×D5×D7
unambiguous semidirect product(C7×D5)⋊(C22×C5)
unambiguous semidirect product(C5×D7)⋊(C22×C5)
unambiguous semidirect productD35⋊(C22×C5)

Splittings

Fitting, socleC2×C52×C7 ⋊ C22
derivedC5×C7 ⋊ C23×C5
HallC52×C7 ⋊ C23
SylowC52 ⋊ C22×D7
SylowC7 ⋊ C22×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2×C5D5×D7
commutator, cosocle, hypocenterC5×C7C23×C5
FrattiniC1G
Fitting, socleC2×C52×C7C22
LCSG ▷ C5×C7
UCSC1 ◁ C2×C5

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 140

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×D5×AGL(1,𝔽7), C2×C5×D7×AGL(1,𝔽5), C4×C5×D5×D7, …
maximal normal subgroup ofC2×C5×D5×AGL(1,𝔽7), C2×C5×D7×AGL(1,𝔽5), C4×C5×D5×D7, …
maximal quotient ofC4×C5×D5×D7, C5×D7×C22⋊D5, C5×D3×D5×D7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1400, 143);