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C3×C13×D29⋊C7 #30629201

order15834
isoclinismisoclinic class of D29⋊C7
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×D29⋊C7
unambiguous semidirect productD29⋊(C3×C7×C13)
unambiguous semidirect product(C3×D29)⋊(C7×C13)
unambiguous semidirect product(C29⋊C7)⋊(C2×C3×C13)
unambiguous semidirect product(C3×C13×D29)⋊C7

Splittings

Fitting, socle, HallC3×C13×C29 ⋊ C2×C7
derived, SylowC29 ⋊ C2×C3×C7×C13
HallC3×C13×C29⋊C7 ⋊ C2
HallC13×C29⋊C7 ⋊ C2×C3
HallC3×C13×D29 ⋊ C7
HallC13×D29 ⋊ C3×C7
HallC3×C29⋊C7 ⋊ C2×C13
HallC13×C29 ⋊ C2×C3×C7
HallC29⋊C7 ⋊ C2×C3×C13
HallC3×D29 ⋊ C7×C13
HallC3×C29 ⋊ C2×C7×C13
HallD29 ⋊ C3×C7×C13

Subgroups

subgroupG/H
center, hypercenterC3×C13D29⋊C7
commutator, cosocle, hypocenterC29C2×C3×C7×C13
FrattiniC1G
Fitting, socleC3×C13×C29C2×C7
LCSG ▷ C29
UCSC1 ◁ C3×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1131

Conjugacy classes & character table

624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C13×AGL(1,𝔽29), C3×#13094090⋊C7, C3×D13×D29⋊C7, …
maximal normal subgroup ofC3×C13×AGL(1,𝔽29), C3×#13094090⋊C7, C3×D13×D29⋊C7, …
maximal quotient ofC3×C13×Dic29⋊C7, C2×C3×C13×D29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15834, 23);