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C3⋊(C43⋊(Dic11⋊C5)) #43248779

order28380
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C43⋊(Dic11⋊C5))
unambiguous semidirect productC43⋊(C3⋊(Dic11⋊C5))
unambiguous semidirect product(C11⋊C5)⋊Dic129
unambiguous semidirect productDic1419⋊C5

Splittings

derived, HallC3×C11×C43 ⋊ C4×C5
HallC3×C43×C11⋊C5 ⋊ C4
HallDic1419 ⋊ C5
HallC43×C11⋊C5 ⋊ Dic3
HallC11×C43 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ Dic43
HallC3×C43 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ Dic129
SylowC43 ⋊ C3⋊(Dic11⋊C5)
HallC3×C11 ⋊ C5×Dic43
SylowC11 ⋊ C5×Dic129
SylowC3 ⋊ C43⋊(Dic11⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊(C43⋊AGL(1,𝔽11))
commutator, hypocenterC3×C11×C43C4×C5
Fitting, socle, cosocleC2×C3×C11×C43C2×C5
prime radicalC2×C3×C43×C11⋊C5C2
LCSG ▷ C3×C11×C43
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5676

Polycyclic presentation:

2,3,5,11,43,2|a^2=f,b^a=b^2,d^a=d^10,e^a=e^42,d^c=d^4

Conjugacy classes & character table

918 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28380, 26);