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C3×(C11⋊C5)⋊Dic29 #34062327

order19140
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C11⋊C5)⋊Dic29
unambiguous semidirect product(C11⋊C5)⋊(C3×Dic29)
unambiguous semidirect productDic319⋊(C3×C5)
unambiguous semidirect product(C3×Dic319)⋊C5

Splittings

derived, HallC11×C29 ⋊ C3×C4×C5
HallC3×C29×C11⋊C5 ⋊ C4
HallC3×Dic319 ⋊ C5
HallC29×C11⋊C5 ⋊ C3×C4
HallDic319 ⋊ C3×C5
HallC3×C11×C29 ⋊ C4×C5
HallC3×C11⋊C5 ⋊ Dic29
HallC3×C29 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3×Dic29
HallC3×C11 ⋊ C5×Dic29
SylowC29 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C3×C5×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C3C29⋊AGL(1,𝔽11)
commutator, hypocenterC11×C29C3×C4×C5
FrattiniC2C3×C29⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C29C2×C5
prime radicalC2×C3×C29×C11⋊C5C2
cosocleC2×C11×C29C2×C3×C5
LCSG ▷ C11×C29
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3828

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19140, 20);