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C5×D29⋊C7 #14523205

order2030
isoclinismisoclinic class of D29⋊C7
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×D29⋊C7
unambiguous semidirect productD29⋊(C5×C7)
unambiguous semidirect product(C29⋊C7)⋊(C2×C5)
unambiguous semidirect product(C5×D29)⋊C7

Splittings

Fitting, socle, HallC5×C29 ⋊ C2×C7
derived, SylowC29 ⋊ C2×C5×C7
HallC5×C29⋊C7 ⋊ C2
HallC5×D29 ⋊ C7
HallC29⋊C7 ⋊ C2×C5
HallD29 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC5D29⋊C7
commutator, cosocle, hypocenterC29C2×C5×C7
FrattiniC1G
Fitting, socleC5×C29C2×C7
LCSG ▷ C29
UCSC1 ◁ C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 145

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3,4,5)(7,11,12,26,19,27,33,8,9,16,18,25,31,34)(10,23,24,28,29,20,21,14,15,32,17,30,13,22);(6,7,10,15,25,16,27,18,30,34,32,21,20,11,17,28,9,13,22,24,33,29,26,31,12,19,23,14,8)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽29), #10596817⋊C7, D5×D29⋊C7, …
maximal normal subgroup ofC5×AGL(1,𝔽29), #10596817⋊C7, D5×D29⋊C7, …
maximal quotient ofC5×Dic29⋊C7, C2×C5×D29⋊C7, C5×D29⋊C49, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2030, 10);