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C2×C3×C3⋊(D101⋊C5) #32911448

order18180
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C3⋊(D101⋊C5)
unambiguous semidirect product(C2×C3)⋊(C3×D101⋊C5)
unambiguous semidirect product(C2×C101⋊C5)⋊(C3×D3)
unambiguous semidirect product(C2×D303)⋊(C3×C5)
unambiguous semidirect product(C2×C3×D303)⋊C5

Splittings

Fitting, socleC2×C32×C101 ⋊ C2×C5
derivedC3×C101 ⋊ C22×C3×C5
HallC32×C101⋊C5 ⋊ C22
HallC2×C3×D303 ⋊ C5
HallC32×C101 ⋊ C22×C5
HallC101⋊C5 ⋊ C2×C3×D3
SylowC101 ⋊ C2×C3×C5×D3
SylowC32 ⋊ C2×D101⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(D101⋊C5)
commutator, cosocle, hypocenterC3×C101C22×C3×C5
FrattiniC1G
Fitting, socleC2×C32×C101C2×C5
LCSG ▷ C3×C101
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1212

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 81);