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C9×D53⋊C13 #27137148

order12402
automorphism?
homologyAbelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC9×D53⋊C13
unambiguous semidirect productD53⋊(C9×C13)
unambiguous semidirect product(C53⋊C13)⋊(C2×C9)
unambiguous semidirect product(C9×D53)⋊C13

Splittings

Fitting, HallC9×C53 ⋊ C2×C13
derived, SylowC53 ⋊ C2×C9×C13
HallC9×C53⋊C13 ⋊ C2
HallC9×D53 ⋊ C13
HallC53⋊C13 ⋊ C2×C9
HallD53 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC9D53⋊C13
commutator, hypocenterC53C2×C9×C13
FrattiniC3C3×D53⋊C13
FittingC9×C53C2×C13
socle, cosocleC3×C53C2×C3×C13
prime radicalC3×D53⋊C13C3
LCSG ▷ C53
UCSC1 ◁ C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 62
transitive degreeμt(G) = 477

A minimal faithful permutation representation — 2 generators on 62 points:

(2,6,7,13,28,44,53,24,51,8,31,32,25,3,4,12,14,26,48,47,41,42,16,17,49,43)(5,19,20,33,11,39,40,29,30,38,27,52,37,9,10,18,36,22,23,50,15,35,34,45,46,21)(54,55,57,56,58,60,59,61,62);(1,2,5,11,24,39,32,17,29,12,25,42,52,53,45,14,4,8,18,34,37,19,35,33,48,26,40,50,28,44,36,30,10,21,38,20,16,6,13,27,47,46,51,43,7,15,31,49,23,41,22,9,3)

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×AGL(1,𝔽53), C9⋊AGL(1,𝔽53), D9×D53⋊C13, …
maximal normal subgroup ofC9×AGL(1,𝔽53), C9⋊AGL(1,𝔽53), D9×D53⋊C13, …
maximal quotient ofC9×Dic53⋊C13, C2×C9×D53⋊C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12402, 11);