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C11×AGL(1,𝔽5)×C43⋊C3 #43248807

order28380
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×AGL(1,𝔽5)×C43⋊C3
unambiguous semidirect product(AGL(1,𝔽5)×C43)⋊(C3×C11)
unambiguous semidirect product(C11×AGL(1,𝔽5)×C43)⋊C3

Splittings

Fitting, socle, HallC5×C11×C43 ⋊ C3×C4
derived, HallC5×C43 ⋊ C3×C4×C11
HallC11×AGL(1,𝔽5)×C43 ⋊ C3
HallC5×C11×C43⋊C3 ⋊ C4
HallAGL(1,𝔽5)×C43 ⋊ C3×C11
HallC5×C43⋊C3 ⋊ C4×C11
HallC11×C43 ⋊ C3×AGL(1,𝔽5)
HallC5×C11 ⋊ C4×C43⋊C3
SylowC43 ⋊ C3×C11×AGL(1,𝔽5)
SylowC5 ⋊ C4×C11×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC11AGL(1,𝔽5)×C43⋊C3
commutator, hypocenterC5×C43C3×C4×C11
FrattiniC1G
Fitting, socleC5×C11×C43C3×C4
prime radicalD5×C11×C43⋊C3C2
cosocleD5×C43C2×C3×C11
LCSG ▷ C5×C43
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28380, 54);