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C3×(C11⋊C5)⋊D71 #37552887

order23430
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C11⋊C5)⋊D71
unambiguous semidirect product(C11⋊C5)⋊(C3×D71)

Splittings

Fitting, socle, HallC3×C11×C71 ⋊ C2×C5
derived, HallC11×C71 ⋊ C2×C3×C5
HallC3×C11⋊C5×C71 ⋊ C2
HallC3×D781 ⋊ C5
HallC11⋊C5×C71 ⋊ C2×C3
HallD781 ⋊ C3×C5
HallC3×C71 ⋊ AGL(1,𝔽11)
HallC3×C11⋊C5 ⋊ D71
SylowC71 ⋊ C3×AGL(1,𝔽11)
HallC11⋊C5 ⋊ C3×D71
HallC3×C11 ⋊ C5×D71
SylowC11 ⋊ C3×C5×D71

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊C5)⋊D71
commutator, cosocle, hypocenterC11×C71C2×C3×C5
FrattiniC1G
Fitting, socleC3×C11×C71C2×C5
LCSG ▷ C11×C71
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2343

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23430, 36);