Finite Group Databasebeta

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D55⋊(C3⋊(D13⋊C3)) #38788111

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

Aliases

unambiguous semidirect productD55⋊(C3⋊(D13⋊C3))
unambiguous semidirect product(D55⋊D39)⋊C3

Splittings

Fitting, socle, derivedC3×C5×C11×C13 ⋊ C22×C3
HallC3×C5×C11×C13⋊C3 ⋊ C22
HallC3×C11×C13⋊C3 ⋊ C2×D5
HallC5×C11×C13 ⋊ C2×C3×D3
HallC3×C5×C13⋊C3 ⋊ C2×D11
HallC11×C13 ⋊ C3×D3×D5
HallC3×C13⋊C3 ⋊ D5×D11
HallC5×C13 ⋊ C3×D3×D11
HallC5×C11 ⋊ C2×C3⋊(D13⋊C3)
SylowC13 ⋊ C3×D15⋊D11
SylowC11 ⋊ D5×C3⋊(D13⋊C3)
SylowC5 ⋊ D11×C3⋊(D13⋊C3)

Subgroups

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

176 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 40 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) = 2145

Polycyclic presentation:

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

Conjugacy classes & character table

345 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 342);