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C2×C3×(D61⋊C3)⋊C5 #24926756

order10980
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×(D61⋊C3)⋊C5
unambiguous semidirect product(D61⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(D61⋊C5)⋊(C2×C32)
unambiguous semidirect product(C2×D61⋊C3)⋊(C3×C5)
unambiguous semidirect product((C61⋊C3)⋊C5)⋊(C22×C3)
unambiguous semidirect product(C2×D61⋊C5)⋊C32
unambiguous semidirect product(C2×(C61⋊C3)⋊C5)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D61⋊C3)⋊C5
unambiguous semidirect product(C2×C3×D61⋊C5)⋊C3

Splittings

Fitting, socleC2×C3×C61 ⋊ C2×C3×C5
derived, SylowC61 ⋊ C22×C32×C5
HallC3×(C61⋊C3)⋊C5 ⋊ C22
HallC2×C3×D61⋊C3 ⋊ C5
HallC2×D61⋊C5 ⋊ C32
HallC3×C61⋊C3 ⋊ C22×C5
HallC61⋊C5 ⋊ C22×C32
HallC2×D61 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3(D61⋊C3)⋊C5
commutator, cosocle, hypocenterC61C22×C32×C5
FrattiniC1G
Fitting, socleC2×C3×C61C2×C3×C5
LCSG ▷ C61
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 106);