Finite Group Databasebeta

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C3×C13⋊(D11⋊C25) #36339698

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

Aliases

direct productC3×C13⋊(D11⋊C25)
unambiguous semidirect product(C11⋊C25)⋊(C3×D13)
unambiguous semidirect product(C3×D143)⋊C25

Splittings

derived, HallC11×C13 ⋊ C2×C3×C25
HallC3×C13×C11⋊C25 ⋊ C2
HallC13×C11⋊C25 ⋊ C2×C3
HallC3×D143 ⋊ C25
HallC3×C11⋊C25 ⋊ D13
HallC3×C11×C13 ⋊ C2×C25
HallD143 ⋊ C3×C25
HallC11⋊C25 ⋊ C3×D13
HallC3×C13 ⋊ D11⋊C25
HallC3×C11 ⋊ C25×D13
SylowC13 ⋊ C3×D11⋊C25
SylowC11 ⋊ C3×C25×D13

Subgroups

subgroupG/H
center, hypercenterC3×C5C13⋊AGL(1,𝔽11)
commutator, hypocenterC11×C13C2×C3×C25
FrattiniC5C3×C13⋊AGL(1,𝔽11)
Fitting, socleC3×C5×C11×C13C2×C5
prime radicalC3×C5×D143C5
cosocleC5×C11×C13C2×C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10725

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21450, 22);