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C7×C5⋊(D31⋊C5) #24925754

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

Aliases

direct productC7×C5⋊(D31⋊C5)
unambiguous semidirect productC5⋊(C7×D31⋊C5)
unambiguous semidirect productΓL(1,𝔽32)⋊(C7×D5)
unambiguous semidirect productD155⋊(C5×C7)
unambiguous semidirect product(C7×D155)⋊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, hypercenterC7C5⋊(D31⋊C5)
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

245 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D5×D31⋊C5, D7×C5⋊(D31⋊C5), D35⋊(D31⋊C5), …
maximal normal subgroup ofC7×D5×D31⋊C5, D7×C5⋊(D31⋊C5), D35⋊(D31⋊C5), …
maximal quotient ofC7×ΓL(1,𝔽32)⋊Dic5, C2×C7×C5⋊(D31⋊C5), C3×C7×C5⋊(D31⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10850, 17);