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D5×C29⋊C7 #14523206

order2030
isoclinismisoclinic class of D5×C29⋊C7
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productD5×C29⋊C7
unambiguous semidirect productC5⋊(C2×C29⋊C7)
unambiguous semidirect product(D5×C29)⋊C7

Splittings

Fitting, socle, derived, HallC5×C29 ⋊ C2×C7
HallC5×C29⋊C7 ⋊ C2
HallD5×C29 ⋊ C7
SylowC29 ⋊ C7×D5
SylowC5 ⋊ C2×C29⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C29C2×C7
LCSG ▷ C5×C29
UCSC1

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10596816⋊C7, AGL(1,𝔽5)×C29⋊C7, D5×D29⋊C7, …
maximal normal subgroup of#10596816⋊C7, AGL(1,𝔽5)×C29⋊C7, D5×D29⋊C7, …
maximal quotient ofDic5×C29⋊C7, C2×D5×C29⋊C7, D5×C29⋊C49, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2030, 11);