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C2×C5×C7×ΓL(1,𝔽32) #24925758

order10850
isoclinismisoclinic class of ΓL(1,𝔽32)
automorphism?
homologyAbelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC2×C5×C7×ΓL(1,𝔽32)
unambiguous semidirect product(C2×C31)⋊(C52×C7)
unambiguous semidirect product(C2×C5×C31)⋊(C5×C7)
unambiguous semidirect product(C2×C7×C31)⋊C52
unambiguous semidirect product(C2×C5×C7×C31)⋊C5

Splittings

Fitting, socleC2×C5×C7×C31 ⋊ C5
derived, SylowC31 ⋊ C2×C52×C7
HallC2×C7×C31 ⋊ C52
HallC7×C31 ⋊ C2×C52
HallC2×C31 ⋊ C52×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7ΓL(1,𝔽32)
commutator, cosocle, hypocenterC31C2×C52×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C31C5
LCSG ▷ C31
UCSC1 ◁ C2×C5×C7

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

770 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C7×Dic31⋊C5, C5×C7⋊(Dic31⋊C5), C5×Dic7×ΓL(1,𝔽32), …
maximal normal subgroup ofC5×C7×Dic31⋊C5, C5×C7⋊(Dic31⋊C5), C5×Dic7×ΓL(1,𝔽32), …
maximal quotient ofC4×C5×C7×ΓL(1,𝔽32), C22×C5×C7×ΓL(1,𝔽32), C5×D3×C7×ΓL(1,𝔽32), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10850, 21);