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C7×D5×ΓL(1,𝔽32) #24925755

order10850
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D5×ΓL(1,𝔽32)
unambiguous semidirect productC5⋊(C2×C7×ΓL(1,𝔽32))
unambiguous semidirect product(D5×C31)⋊(C5×C7)
unambiguous semidirect product(C7×D5×C31)⋊C5

Splittings

Fitting, socleC5×C7×C31 ⋊ C2×C5
derivedC5×C31 ⋊ C2×C5×C7
HallC5×C7×ΓL(1,𝔽32) ⋊ C2
HallC5×ΓL(1,𝔽32) ⋊ C2×C7
HallC7×C31 ⋊ C5×D5
SylowC31 ⋊ C5×C7×D5

Subgroups

subgroupG/H
center, hypercenterC7D5×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC5×C31C2×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C31C2×C5
LCSG ▷ C5×C31
UCSC1 ◁ C7

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×ΓL(1,𝔽32)⋊AGL(1,𝔽5), C7×AGL(1,𝔽5)×ΓL(1,𝔽32), C7⋊(ΓL(1,𝔽32)⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC7×ΓL(1,𝔽32)⋊AGL(1,𝔽5), C7×AGL(1,𝔽5)×ΓL(1,𝔽32), C7⋊(ΓL(1,𝔽32)⋊AGL(1,𝔽5)), …
maximal quotient ofC7×Dic5×ΓL(1,𝔽32), C2×C7×D5×ΓL(1,𝔽32), C3×C7×D5×ΓL(1,𝔽32), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10850, 18);