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C3⋊D429 #14579481

order2574
isoclinismisoclinic class of C3⋊D429
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊D429
unambiguous semidirect productC11⋊(C3⋊D39)
unambiguous semidirect productC13⋊(C3⋊D33)

Splittings

Fitting, socle, derived, HallC32×C11×C13 ⋊ C2
HallC11×C13 ⋊ C3⋊D3
HallC32×C13 ⋊ D11
HallC32×C11 ⋊ D13
SylowC13 ⋊ C3⋊D33
SylowC11 ⋊ C3⋊D39
SylowC32 ⋊ D143

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C13C2
LCSG ▷ C32×C11×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1287

Polycyclic presentation:

2,3^2,11,13|b^a=b^2,c^a=c^2,d^a=d^10,e^a=e^12

Conjugacy classes & character table

645 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3⋊(C3⋊(C13⋊AGL(1,𝔽11))), C3⋊D2145, C5×C3⋊D429, …
maximal normal subgroup ofC3⋊(C3⋊(C13⋊AGL(1,𝔽11))), C5×C3⋊D429, C7×C3⋊D429, …
maximal quotient ofC3⋊D2145, C5×C3⋊D429, C3⋊D3003, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2574, 32);