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C2×C5×D5×ΓL(1,𝔽8) #14523617

order2100
isoclinismisoclinic class of D5×ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D5×ΓL(1,𝔽8)
unambiguous semidirect productC5⋊(C22×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C5)⋊(C2×C5×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D5)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C7×D5)⋊C3

Splittings

Fitting, socleC2×C52×C7 ⋊ C2×C3
derivedC5×C7 ⋊ C22×C3×C5
HallC2×C5×C7×D5 ⋊ C3
HallC52×ΓL(1,𝔽8) ⋊ C22
HallC52×C7 ⋊ C22×C3
SylowC52 ⋊ C22×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C3×C5×D5

Subgroups

subgroupG/H
center, hypercenterC2×C5D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C22×C3×C5
FrattiniC1G
Fitting, socleC2×C52×C7C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C5

96 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×C49⋊C3, C5×D5×#64423, C5×D5×#64422, …
maximal normal subgroup ofC2×C5×C7×D5×ΓL(1,𝔽8), C2×C5×D5×C11×ΓL(1,𝔽8), C2×C5×D5×C13×ΓL(1,𝔽8), …
maximal quotient ofC2×C5×D5×C49⋊C3, C5×D5×#64423, C5×D5×#64422, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 97);