Finite Group Databasebeta

← Prev (#27137160) Next (#27137162) →

C3×C53×D13⋊C3 #27137161

order12402
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C53 · Schur multiplier (H2) = C3

Aliases

direct productC3×C53×D13⋊C3
unambiguous semidirect productD13⋊(C32×C53)
unambiguous semidirect product(C13⋊C3)⋊(C2×C3×C53)
unambiguous semidirect product(C3×D13)⋊(C3×C53)
unambiguous semidirect product(D13×C53)⋊C32
unambiguous semidirect product(C3×D13×C53)⋊C3

Splittings

Fitting, socleC3×C13×C53 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C32×C53
HallC3×C13⋊C3×C53 ⋊ C2
HallD13×C53 ⋊ C32
HallC13×C53 ⋊ C2×C32
HallC3×C13⋊C3 ⋊ C2×C53
HallD13 ⋊ C32×C53

Subgroups

subgroupG/H
center, hypercenterC3×C53D13⋊C3
commutator, cosocle, hypocenterC13C2×C32×C53
FrattiniC1G
Fitting, socleC3×C13×C53C2×C3
LCSG ▷ C13
UCSC1 ◁ C3×C53

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 69
transitive degreeμt(G) = 2067

A minimal faithful permutation representation — 2 generators on 69 points:

(2,6,7,3,4,8)(5,12,11,9,10,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(1,2,5,4,8,11,10,12,13,7,6,9,3)(67,68,69)

Conjugacy classes & character table

1272 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C53×AGL(1,𝔽13), C3×#14583754⋊C3, C3×D13⋊C3×D53, …
maximal normal subgroup ofC3×C53×AGL(1,𝔽13), C3×#14583754⋊C3, C3×D13⋊C3×D53, …
maximal quotient ofC3×C53×Dic13⋊C3, C2×C3×C53×D13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12402, 24);