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C2×C3⋊(C5⋊(D67⋊C3)) #27130409

order12060
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(C5⋊(D67⋊C3))
unambiguous semidirect product(C2×C3)⋊(C5⋊(D67⋊C3))
unambiguous semidirect product(C2×C5)⋊(C3⋊(D67⋊C3))
unambiguous semidirect product(C2×C67⋊C3)⋊D15
unambiguous semidirect product(C2×D1005)⋊C3

Splittings

Fitting, socleC2×C3×C5×C67 ⋊ C2×C3
derivedC3×C5×C67 ⋊ C22×C3
HallC3×C5×C67⋊C3 ⋊ C22
HallC3×C67⋊C3 ⋊ C2×D5
HallC5×C67 ⋊ C2×C3×D3
SylowC67 ⋊ C2×C3×D15
SylowC5 ⋊ C2×C3⋊(D67⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊(D67⋊C3))
commutator, cosocle, hypocenterC3×C5×C67C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C67C2×C3
LCSG ▷ C3×C5×C67
UCSC1 ◁ C2

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

384 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12060, 79);