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C13⋊((C11⋊C5)⋊D11) #30628515

order15730
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC13⋊((C11⋊C5)⋊D11)
unambiguous semidirect product(C11⋊C5)⋊D143

Splittings

Fitting, socle, derived, HallC112×C13 ⋊ C2×C5
HallC11×C13×C11⋊C5 ⋊ C2
HallC11⋊D143 ⋊ C5
HallC11×C11⋊C5 ⋊ D13
SylowC112 ⋊ C5×D13
SylowC13 ⋊ (C11⋊C5)⋊D11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC112×C13C2×C5
LCSG ▷ C112×C13
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 715

Polycyclic presentation:

2,5,11^2,13|c^a=c^10,d^a=d^10,e^a=e^12,c^b=c^4

Conjugacy classes & character table

508 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×(C11⋊C5)⋊D11, D11×C13⋊AGL(1,𝔽11), AGL(1,𝔽11)×D143, …
maximal normal subgroup ofD13×(C11⋊C5)⋊D11, D11×C13⋊AGL(1,𝔽11), AGL(1,𝔽11)×D143, …
maximal quotient of(C11⋊C5)⋊Dic143, C2×C13⋊((C11⋊C5)⋊D11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15730, 32);