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C2×C3⋊((D61⋊C3)⋊C5) #24926757

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

Aliases

direct productC2×C3⋊((D61⋊C3)⋊C5)
unambiguous semidirect product(C2×C3)⋊((D61⋊C3)⋊C5)
unambiguous semidirect product(C2×(C61⋊C3)⋊C5)⋊D3
unambiguous semidirect product(C2×C3⋊(D61⋊C3))⋊C5
unambiguous semidirect product(C2×C3⋊(D61⋊C5))⋊C3

Splittings

Fitting, socleC2×C3×C61 ⋊ C2×C3×C5
derivedC3×C61 ⋊ C22×C3×C5
HallC3×(C61⋊C3)⋊C5 ⋊ C22
HallC2×C3⋊(D61⋊C3) ⋊ C5
HallC3×C61⋊C3 ⋊ C22×C5
HallC61⋊C5 ⋊ C2×C3×D3
SylowC61 ⋊ C2×C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC2C3⋊((D61⋊C3)⋊C5)
commutator, cosocle, hypocenterC3×C61C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C61C2×C3×C5
LCSG ▷ C3×C61
UCSC1 ◁ C2

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 107);