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C5×C7⋊(D31⋊C5) #24925752

order10850
automorphism?
homologyAbelianization (H1) = C2×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7⋊(D31⋊C5)
unambiguous semidirect productC7⋊(C5×D31⋊C5)
unambiguous semidirect productΓL(1,𝔽32)⋊(C5×D7)
unambiguous semidirect productD217⋊C52
unambiguous semidirect product(C5×D217)⋊C5

Splittings

Fitting, socleC5×C7×C31 ⋊ C2×C5
derived, HallC7×C31 ⋊ C2×C52
HallC5×C7×ΓL(1,𝔽32) ⋊ C2
HallC5×ΓL(1,𝔽32) ⋊ D7
HallD217 ⋊ C52
SylowC31 ⋊ C52×D7
SylowC7 ⋊ C5×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC5C7⋊(D31⋊C5)
commutator, cosocle, hypocenterC7×C31C2×C52
FrattiniC1G
Fitting, socleC5×C7×C31C2×C5
LCSG ▷ C7×C31
UCSC1 ◁ C5

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D7×D31⋊C5, D5×C7⋊(D31⋊C5), D35⋊(D31⋊C5), …
maximal normal subgroup ofC5×D7×D31⋊C5, D5×C7⋊(D31⋊C5), D35⋊(D31⋊C5), …
maximal quotient ofC5×C7⋊(Dic31⋊C5), C2×C5×C7⋊(D31⋊C5), C3×C5×C7⋊(D31⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10850, 15);