Finite Group Databasebeta

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C3×C5×C22⋊(C112⋊C3) #36345371

order21780
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3×C11

Aliases

direct productC3×C5×C22⋊(C112⋊C3)
unambiguous semidirect product(C22×C3)⋊(C5×C112⋊C3)
unambiguous semidirect product(C22×C3×C5)⋊(C112⋊C3)
unambiguous semidirect product(C3×C5×C112)⋊A4

Splittings

Fitting, socleC22×C3×C5×C112 ⋊ C3
derived, HallC22×C112 ⋊ C32×C5
HallC22×C5×C112 ⋊ C32
HallC5×C112 ⋊ C3×A4
SylowC112 ⋊ C3×C5×A4
HallC22×C5 ⋊ C3×C112⋊C3
SylowC22 ⋊ C3×C5×C112⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊(C112⋊C3)
commutator, cosocle, hypocenterC22×C112C32×C5
FrattiniC1G
Fitting, socleC22×C3×C5×C112C3
LCSG ▷ C22×C112
UCSC1 ◁ C3×C5

136 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 720);