Finite Group Databasebeta

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C3⋊(C11⋊#10596815) #34062386

order19140
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C11⋊#10596815)
unambiguous semidirect productC11⋊(C3⋊#10596815)

Splittings

Fitting, socle, derived, HallC3×C5×C11×C29 ⋊ C4
HallC5×C11×C29 ⋊ Dic3
HallC3×C11×C29 ⋊ AGL(1,𝔽5)
HallC3×C5×C29 ⋊ Dic11
HallC11×C29 ⋊ ΓL(1,𝔽16)
HallC3×C5×C11 ⋊ #1181
HallC5×C29 ⋊ Dic33
HallC3×C29 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ C3⋊#1181
HallC3×C11 ⋊ #10596815
SylowC29 ⋊ C3⋊(C11⋊AGL(1,𝔽5))
HallC3×C5 ⋊ C11⋊#1181
SylowC11 ⋊ C3⋊#10596815
SylowC5 ⋊ C3⋊(C11⋊#1181)
SylowC3 ⋊ C11⋊#10596815

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C11×C29C4
prime radical, cosocleC3×C11×D145C2
LCSG ▷ C3×C5×C11×C29
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4785

Polycyclic presentation:

2^2,3,5,11,29|a^2=b,c^a=c^2,d^a=d^2,e^a=e^10,f^a=f^12,d^b=d^4,f^b=f^28

Conjugacy classes & character table

1224 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 79);