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C3×C13⋊C3×C11⋊AGL(1,𝔽5) #38788066

order25740
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C13⋊C3×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(C3×AGL(1,𝔽5)×C13⋊C3)
unambiguous semidirect product(C13×C11⋊AGL(1,𝔽5))⋊C32
unambiguous semidirect product(C3×C13×C11⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, socleC3×C5×C11×C13 ⋊ C3×C4
derived, HallC5×C11×C13 ⋊ C32×C4
HallC3×C5×C11×C13⋊C3 ⋊ C4
HallC13×C11⋊AGL(1,𝔽5) ⋊ C32
HallC3×C11×C13⋊C3 ⋊ AGL(1,𝔽5)
HallC3×C5×C13⋊C3 ⋊ Dic11
HallC11×C13 ⋊ C32×AGL(1,𝔽5)
HallC5×C13 ⋊ C32×Dic11
HallC5×C11 ⋊ C3×C4×C13⋊C3
SylowC13 ⋊ C32×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ C3×AGL(1,𝔽5)×C13⋊C3
SylowC5 ⋊ C3×C13⋊C3×Dic11

Subgroups

subgroupG/H
center, hypercenterC3C13⋊C3×C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11×C13C32×C4
FrattiniC1G
Fitting, socleC3×C5×C11×C13C3×C4
prime radicalC3×D5×C11×C13⋊C3C2
cosocleD5×C11×C13C2×C32
LCSG ▷ C5×C11×C13
UCSC1 ◁ C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2145

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 297);