Finite Group Databasebeta

← Prev (#17985303) Next (#17985305) →

C29×AGL(1,𝔽13) #17985304

order4524
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C3×C4×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C29)
unambiguous semidirect product(C29×#261)⋊C3

Splittings

Fitting, socle, HallC13×C29 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C29
HallC29×#261 ⋊ C3
HallC29×C13⋊C3 ⋊ C4
Hall#261 ⋊ C3×C29
HallC13⋊C3 ⋊ C4×C29

Subgroups

subgroupG/H
center, hypercenterC29AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C29
FrattiniC1G
Fitting, socleC13×C29C3×C4
prime radicalC29×D13⋊C3C2
cosocleD13C2×C3×C29
LCSG ▷ C13
UCSC1 ◁ C29

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 377

A minimal faithful permutation representation — 2 generators on 42 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(31,36,40,37,33,42,34,35,38,32,39,41);(30,31,35,33,40,37,41,42,32,38,39,36,34)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C29×AGL(1,𝔽13), C29×C3⋊AGL(1,𝔽13), C5×C29×AGL(1,𝔽13), …
maximal normal subgroup ofC3×C29×AGL(1,𝔽13), C5×C29×AGL(1,𝔽13), AGL(1,𝔽13)×C29⋊C7, …
maximal quotient ofC29×#261⋊C9, C3×C29×AGL(1,𝔽13), C29×C3⋊AGL(1,𝔽13), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4524, 14);