Finite Group Databasebeta

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C3×C13×D11⋊C25 #36339697

order21450
automorphism?
homologyAbelianization (H1) = C2×C3×C13×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×D11⋊C25
unambiguous semidirect productD11⋊(C3×C13×C25)
unambiguous semidirect product(C3×D11)⋊(C13×C25)
unambiguous semidirect product(C11⋊C25)⋊(C2×C3×C13)
unambiguous semidirect product(C3×C13×D11)⋊C25

Splittings

derived, SylowC11 ⋊ C2×C3×C13×C25
HallC3×C13×C11⋊C25 ⋊ C2
HallC13×C11⋊C25 ⋊ C2×C3
HallC3×C13×D11 ⋊ C25
HallC3×C11⋊C25 ⋊ C2×C13
HallC3×C11×C13 ⋊ C2×C25
HallC13×D11 ⋊ C3×C25
HallC11⋊C25 ⋊ C2×C3×C13
HallC11×C13 ⋊ C2×C3×C25
HallC3×D11 ⋊ C13×C25
HallC3×C11 ⋊ C2×C13×C25
HallD11 ⋊ C3×C13×C25

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13AGL(1,𝔽11)
commutator, hypocenterC11C2×C3×C13×C25
FrattiniC5C3×C13×AGL(1,𝔽11)
Fitting, socleC3×C5×C11×C13C2×C5
prime radicalC3×C5×C13×D11C5
cosocleC5×C11C2×C3×C5×C13
LCSG ▷ C11
UCSC1 ◁ C3×C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10725

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 21);