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C3⋊Dic3135 #49178479

order37620
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊Dic3135
unambiguous semidirect productC11⋊(C3⋊Dic285)
unambiguous semidirect productC19⋊(C3⋊Dic165)

Splittings

derived, HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ Dic5
HallC5×C11×C19 ⋊ C3⋊Dic3
HallC32×C5×C19 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic19
HallC11×C19 ⋊ C3⋊Dic15
HallC32×C19 ⋊ Dic55
HallC32×C11 ⋊ Dic95
HallC5×C19 ⋊ C3⋊Dic33
HallC5×C11 ⋊ C3⋊Dic57
HallC32×C5 ⋊ Dic209
SylowC19 ⋊ C3⋊Dic165
SylowC11 ⋊ C3⋊Dic285
SylowC32 ⋊ Dic1045
SylowC5 ⋊ C3⋊Dic627

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊D3135
commutator, hypocenterC32×C5×C11×C19C4
Fitting, socle, prime radical, cosocleC2×C32×C5×C11×C19C2
LCSG ▷ C32×C5×C11×C19
UCSC1 ◁ C2

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Polycyclic presentation:

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

Conjugacy classes & character table

9408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 188);