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C3⋊(C13⋊(D11⋊C25)) #36339702

order21450
automorphism?
homologyAbelianization (H1) = C2×C25 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C13⋊(D11⋊C25))
unambiguous semidirect productC13⋊(C3⋊(D11⋊C25))
unambiguous semidirect product(C11⋊C25)⋊D39
unambiguous semidirect productD429⋊C25

Splittings

derived, HallC3×C11×C13 ⋊ C2×C25
HallC3×C13×C11⋊C25 ⋊ C2
HallC13×C11⋊C25 ⋊ D3
HallD429 ⋊ C25
HallC3×C11⋊C25 ⋊ D13
HallC11⋊C25 ⋊ D39
HallC11×C13 ⋊ D3×C25
HallC3×C13 ⋊ D11⋊C25
HallC3×C11 ⋊ C25×D13
SylowC13 ⋊ C3⋊(D11⋊C25)
SylowC11 ⋊ C25×D39
SylowC3 ⋊ C13⋊(D11⋊C25)

Subgroups

subgroupG/H
center, Frattini, hypercenterC5C3⋊(C13⋊AGL(1,𝔽11))
commutator, hypocenterC3×C11×C13C2×C25
Fitting, socle, cosocleC3×C5×C11×C13C2×C5
prime radicalC5×D429C5
LCSG ▷ C3×C11×C13
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10725

Polycyclic presentation:

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

Conjugacy classes & character table

720 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 26);