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C2×C5⋊(#66526⋊C2) #20269089

order6660
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(#66526⋊C2)
unambiguous semidirect product(C2×C5)⋊(#66526⋊C2)
unambiguous semidirect product(C2×#66526)⋊D5

Splittings

Fitting, socleC2×C5×C37 ⋊ C2×C9
derived, HallC5×C37 ⋊ C22×C9
HallC5×#66526 ⋊ C22
HallC2×D185 ⋊ C9
Hall#66526 ⋊ C2×D5
SylowC37 ⋊ C2×C9×D5
SylowC5 ⋊ C2×#66526⋊C2

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(#66526⋊C2)
commutator, hypocenterC5×C37C22×C9
FrattiniC1G
Fitting, socleC2×C5×C37C2×C9
LCSG ▷ C5×C37
UCSC1 ◁ C2

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C25⋊(#66526⋊C2), D5×C5⋊(#66526⋊C2), C2×C5×C5⋊(#66526⋊C2), …
maximal normal subgroup ofC2×C5×C5⋊(#66526⋊C2)
maximal quotient ofC2×C25⋊(#66526⋊C2), D5×C5⋊(#66526⋊C2), C2×C5×C5⋊(#66526⋊C2), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6660, 86);