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C32×D29⋊C7 #16814501

order3654
isoclinismisoclinic class of D29⋊C7
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×D29⋊C7
unambiguous semidirect productD29⋊(C32×C7)
unambiguous semidirect product(C3×D29)⋊(C3×C7)
unambiguous semidirect product(C29⋊C7)⋊(C2×C32)
unambiguous semidirect product(C32×D29)⋊C7

Splittings

Fitting, socle, HallC32×C29 ⋊ C2×C7
derived, SylowC29 ⋊ C2×C32×C7
HallC32×C29⋊C7 ⋊ C2
HallC32×D29 ⋊ C7
HallC29⋊C7 ⋊ C2×C32
HallD29 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC32D29⋊C7
commutator, cosocle, hypocenterC29C2×C32×C7
FrattiniC1G
Fitting, socleC32×C29C2×C7
LCSG ▷ C29
UCSC1 ◁ C32

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 261

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3)(8,12,13,27,20,28,34,9,10,17,19,26,32,35)(11,24,25,29,30,21,22,15,16,33,18,31,14,23);(4,5,6)(7,8,11,16,26,17,28,19,31,35,33,22,21,12,18,29,10,14,23,25,34,30,27,32,13,20,24,15,9)

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×C5×D29⋊C7, C32×C5⋊(D29⋊C7), C3×ΓL(1,𝔽8)⋊(D29⋊C7), …
maximal normal subgroup ofC32×C5×D29⋊C7, C32×C7×D29⋊C7
maximal quotient ofC32×C5×D29⋊C7, C32×C5⋊(D29⋊C7), C32×D29⋊C49, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3654, 18);