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C3×D29⋊C7 #11927384

order1218
isoclinismisoclinic class of D29⋊C7
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC3D29⋊C7
commutator, cosocle, hypocenterC29C2×C3×C7
FrattiniC1G
Fitting, socleC3×C29C2×C7
LCSG ▷ C29
UCSC1 ◁ C3

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 87

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×AGL(1,𝔽29), C3⋊AGL(1,𝔽29), D3×D29⋊C7, …
maximal normal subgroup ofC3×AGL(1,𝔽29), C3⋊AGL(1,𝔽29), D3×D29⋊C7, …
maximal quotient ofC3×Dic29⋊C7, C2×C3×D29⋊C7, C9×D29⋊C7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1218, 1);