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C52×D29⋊C7 #23778908

order10150
isoclinismisoclinic class of D29⋊C7
automorphism?
homologyAbelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC52×D29⋊C7
unambiguous semidirect productD29⋊(C52×C7)
unambiguous semidirect product(C29⋊C7)⋊(C2×C52)
unambiguous semidirect product(C5×D29)⋊(C5×C7)
unambiguous semidirect product(C52×D29)⋊C7

Splittings

Fitting, socle, HallC52×C29 ⋊ C2×C7
derived, SylowC29 ⋊ C2×C52×C7
HallC52×C29⋊C7 ⋊ C2
HallC52×D29 ⋊ C7
HallC29⋊C7 ⋊ C2×C52
HallD29 ⋊ C52×C7

Subgroups

subgroupG/H
center, hypercenterC52D29⋊C7
commutator, cosocle, hypocenterC29C2×C52×C7
FrattiniC1G
Fitting, socleC52×C29C2×C7
LCSG ▷ C29
UCSC1 ◁ C52

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

400 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC52×AGL(1,𝔽29), C5×#10596817⋊C7, C5×D5×D29⋊C7, …
maximal normal subgroup ofC52×AGL(1,𝔽29), C5×#10596817⋊C7, C5×D5×D29⋊C7, …
maximal quotient ofC52×Dic29⋊C7, C2×C52×D29⋊C7, C3×C52×D29⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10150, 14);