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C2×C5⋊(D67⋊C9) #27130348

order12060
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(D67⋊C9)
unambiguous semidirect product(C2×C5)⋊(D67⋊C9)
unambiguous semidirect product(C2×C67⋊C9)⋊D5
unambiguous semidirect product(C2×D335)⋊C9

Splittings

derived, HallC5×C67 ⋊ C22×C9
HallC5×C67⋊C9 ⋊ C22
HallC2×D335 ⋊ C9
HallC67⋊C9 ⋊ C2×D5
SylowC67 ⋊ C2×C9×D5
SylowC5 ⋊ C2×D67⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D67⋊C3)
commutator, hypocenterC5×C67C22×C9
FrattiniC3C2×C5⋊(D67⋊C3)
Fitting, socleC2×C3×C5×C67C2×C3
prime radicalC2×C3×D335C3
cosocleC3×C5×C67C22×C3
LCSG ▷ C5×C67
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

402 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12060, 18);