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C3×C4×(C112⋊C3)⋊C5 #36344969

order21780
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C4×(C112⋊C3)⋊C5
unambiguous semidirect product(C4×C112⋊C3)⋊(C3×C5)
unambiguous semidirect product(C4×#10597243)⋊C32
unambiguous semidirect product(C3×C4×C112⋊C3)⋊C5
unambiguous semidirect product(C3×C4×#10597243)⋊C3

Splittings

FittingC3×C4×C112 ⋊ C3×C5
derived, SylowC112 ⋊ C32×C4×C5
HallC3×C4×C112⋊C3 ⋊ C5
HallC4×#10597243 ⋊ C32
HallC3×C112⋊C3 ⋊ C4×C5
Hall#10597243 ⋊ C32×C4
HallC4×C112 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C4(C112⋊C3)⋊C5
commutator, hypocenterC112C32×C4×C5
FrattiniC2C2×C3×(C112⋊C3)⋊C5
FittingC3×C4×C112C3×C5
socleC2×C3×C112C2×C3×C5
prime radicalC2×C3×(C112⋊C3)⋊C5C2
cosocleC2×C112C2×C32×C5
LCSG ▷ C112
UCSC1 ◁ C3×C4

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

276 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 318);