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C3×(C23⋊C11)⋊AGL(1,𝔽5) #29503248

order15180
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C23⋊C11)⋊AGL(1,𝔽5)
unambiguous semidirect product(C23⋊C11)⋊(C3×AGL(1,𝔽5))
unambiguous semidirect product(C23⋊AGL(1,𝔽5))⋊(C3×C11)
unambiguous semidirect product(C3×C23⋊AGL(1,𝔽5))⋊C11

Splittings

Fitting, socle, HallC3×C5×C23 ⋊ C4×C11
derived, HallC5×C23 ⋊ C3×C4×C11
HallC3×C5×C23⋊C11 ⋊ C4
HallC3×C23⋊AGL(1,𝔽5) ⋊ C11
HallC5×C23⋊C11 ⋊ C3×C4
HallC3×C23⋊C11 ⋊ AGL(1,𝔽5)
HallC23⋊AGL(1,𝔽5) ⋊ C3×C11
HallC23⋊C11 ⋊ C3×AGL(1,𝔽5)
HallC3×C23 ⋊ C11×AGL(1,𝔽5)
SylowC23 ⋊ C3×C11×AGL(1,𝔽5)
HallC3×C5 ⋊ Dic23⋊C11
SylowC5 ⋊ C3×Dic23⋊C11

Subgroups

subgroupG/H
center, hypercenterC3(C23⋊C11)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C23C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C23C4×C11
prime radicalC3×D5×C23⋊C11C2
cosocleD5×C23C2×C3×C11
LCSG ▷ C5×C23
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 345

Conjugacy classes & character table

177 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15180, 34);