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C11⋊((C43⋊C3)⋊Dic5) #43248786

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

Aliases

unambiguous semidirect productC11⋊((C43⋊C3)⋊Dic5)
unambiguous semidirect product(C43⋊C3)⋊Dic55
unambiguous semidirect productDic2365⋊C3

Splittings

derived, HallC5×C11×C43 ⋊ C3×C4
HallDic2365 ⋊ C3
HallC5×C11×C43⋊C3 ⋊ C4
HallC11×C43⋊C3 ⋊ Dic5
HallC5×C43⋊C3 ⋊ Dic11
HallC11×C43 ⋊ C3×Dic5
HallC5×C43 ⋊ C3×Dic11
HallC43⋊C3 ⋊ Dic55
HallC5×C11 ⋊ (C43⋊C3)⋊C4
SylowC43 ⋊ C3×Dic55
SylowC11 ⋊ (C43⋊C3)⋊Dic5
SylowC5 ⋊ C11⋊((C43⋊C3)⋊C4)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C5⋊(C11⋊(D43⋊C3))
commutator, hypocenterC5×C11×C43C3×C4
Fitting, socle, cosocleC2×C5×C11×C43C2×C3
prime radicalC2×C5×C11×C43⋊C3C2
LCSG ▷ C5×C11×C43
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9460

Polycyclic presentation:

2,3,5,11,43,2|a^2=f,c^a=c^4,d^a=d^10,e^a=e^42,e^b=e^36

Conjugacy classes & character table

944 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28380, 33);