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C29×C22⋊(C13⋊C3) #17985335

order4524
isoclinismisoclinic class of C22⋊(C13⋊C3)
automorphism?
homologyAbelianization (H1) = C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productC29×C22⋊(C13⋊C3)
unambiguous semidirect productC22⋊(C29×C13⋊C3)
unambiguous semidirect productC13⋊(A4×C29)
unambiguous semidirect product(C22×C29)⋊(C13⋊C3)
unambiguous semidirect product(C13×C29)⋊A4

Splittings

Fitting, socle, HallC22×C13×C29 ⋊ C3
derived, HallC22×C13 ⋊ C3×C29
HallC13×C29 ⋊ A4
HallC22×C29 ⋊ C13⋊C3
SylowC13 ⋊ A4×C29
SylowC22 ⋊ C29×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC29C22⋊(C13⋊C3)
commutator, cosocle, hypocenterC22×C13C3×C29
FrattiniC1G
Fitting, socleC22×C13×C29C3
LCSG ▷ C22×C13
UCSC1 ◁ C29

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 1508

A minimal faithful permutation representation — 2 generators on 46 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)(31,32,33)(35,36,38)(37,40,43)(39,42,41)(44,46,45);(30,33)(31,32)(34,35,37,36,39,43,40,44,46,38,41,45,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofA4×C29×C13⋊C3, C3×C29×C22⋊(C13⋊C3), C5×C29×C22⋊(C13⋊C3), …
maximal normal subgroup ofA4×C29×C13⋊C3, C3×C29×C22⋊(C13⋊C3), C5×C29×C22⋊(C13⋊C3), …
maximal quotient ofC29×C22⋊(C13⋊C9), C3×C29×C22⋊(C13⋊C3), C5×C29×C22⋊(C13⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4524, 45);