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(C3⋊(D13⋊C3))⋊AGL(1,𝔽11) #38788006

order25740
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product(C3⋊(D13⋊C3))⋊AGL(1,𝔽11)
unambiguous semidirect product(C3⋊AGL(1,𝔽11))⋊(D13⋊C3)
unambiguous semidirect product((C13⋊C3)⋊AGL(1,𝔽11))⋊D3
unambiguous semidirect product(D33⋊(D13⋊C3))⋊C5
unambiguous semidirect product(D39⋊AGL(1,𝔽11))⋊C3

Splittings

Fitting, socle, derivedC3×C11×C13 ⋊ C22×C3×C5
HallC3×C13⋊C3×C11⋊C5 ⋊ C22
HallD33⋊(D13⋊C3) ⋊ C5
HallC3×C11×C13⋊C3 ⋊ C22×C5
HallC13×C11⋊C5 ⋊ C2×C3×D3
HallC11×C13 ⋊ C2×C3×C5×D3
HallC3×C13⋊C3 ⋊ C2×AGL(1,𝔽11)
HallC11⋊C5 ⋊ D3×D13⋊C3
SylowC13 ⋊ C3×D3×AGL(1,𝔽11)
SylowC11 ⋊ C5×D3×D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C13C22×C3×C5
LCSG ▷ C3×C11×C13
UCSC1

176 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 429

Polycyclic presentation:

2^2,3,5,3,11,13|f^a=f^10,g^a=g^12,e^b=e^2,f^b=f^10,g^c=g^3,f^d=f^4

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 237);