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C2×C32×D101⋊C5 #32911447

order18180
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×D101⋊C5
unambiguous semidirect productD101⋊(C2×C32×C5)
unambiguous semidirect product(C2×D101)⋊(C32×C5)
unambiguous semidirect product(C101⋊C5)⋊(C22×C32)
unambiguous semidirect product(C2×C101⋊C5)⋊(C2×C32)
unambiguous semidirect product(C2×C3×D101)⋊(C3×C5)
unambiguous semidirect product(C2×C32×D101)⋊C5

Splittings

Fitting, socleC2×C32×C101 ⋊ C2×C5
derived, SylowC101 ⋊ C22×C32×C5
HallC32×C101⋊C5 ⋊ C22
HallC2×C32×D101 ⋊ C5
HallC32×C101 ⋊ C22×C5
HallC101⋊C5 ⋊ C22×C32
HallC2×D101 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32D101⋊C5
commutator, cosocle, hypocenterC101C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C101C2×C5
LCSG ▷ C101
UCSC1 ◁ C2×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1818

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 80);