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C9⋊(C19⋊(Dic11⋊C5)) #49178317

order37620
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC9⋊(C19⋊(Dic11⋊C5))
unambiguous semidirect productC19⋊(C9⋊(Dic11⋊C5))
unambiguous semidirect product(C11⋊C5)⋊Dic171
unambiguous semidirect productDic1881⋊C5

Splittings

derived, HallC9×C11×C19 ⋊ C4×C5
HallC9×C19×C11⋊C5 ⋊ C4
HallDic1881 ⋊ C5
HallC19×C11⋊C5 ⋊ Dic9
HallC9×C11⋊C5 ⋊ Dic19
HallC11×C19 ⋊ C5×Dic9
HallC9×C19 ⋊ Dic11⋊C5
HallC9×C11 ⋊ C5×Dic19
HallC11⋊C5 ⋊ Dic171
SylowC19 ⋊ C9⋊(Dic11⋊C5)
SylowC11 ⋊ C5×Dic171
SylowC9 ⋊ C19⋊(Dic11⋊C5)

Subgroups

subgroupG/H
center, hypercenterC2C9⋊(C19⋊AGL(1,𝔽11))
commutator, hypocenterC9×C11×C19C4×C5
FrattiniC2×C3C3⋊(C19⋊AGL(1,𝔽11))
Fitting, cosocleC2×C9×C11×C19C2×C5
socleC2×C3×C11×C19C5×D3
prime radicalC2×C3×C19×C11⋊C5D3
LCSG ▷ C9×C11×C19
UCSC1 ◁ C2

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7524

Polycyclic presentation:

2,3,5,11,19,2,3|a^2=f,b^3=g^2,b^a=b^2g,d^a=d^10,e^a=e^18,g^a=g^2,d^c=d^4

Conjugacy classes & character table

1212 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 26);