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C2×C5×D609 #27131819

order12180
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D609
unambiguous semidirect product(C2×C3)⋊(C5×D203)
unambiguous semidirect product(C2×C7)⋊(C5×D87)
unambiguous semidirect product(C2×C29)⋊(C5×D21)

Splittings

Fitting, socleC2×C3×C5×C7×C29 ⋊ C2
derived, HallC3×C7×C29 ⋊ C22×C5
HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C2×D3
HallC3×C5×C29 ⋊ C2×D7
HallC7×C29 ⋊ C2×C5×D3
HallC5×C29 ⋊ C2×D21
HallC3×C5×C7 ⋊ C2×D29
HallC3×C29 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×D87
SylowC29 ⋊ C2×C5×D21
HallC3×C7 ⋊ C2×C5×D29
HallC3×C5 ⋊ C2×D203
SylowC7 ⋊ C2×C5×D87
SylowC3 ⋊ C2×C5×D203

Subgroups

subgroupG/H
center, hypercenterC2×C5D609
commutator, hypocenterC3×C7×C29C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C29C2
LCSG ▷ C3×C7×C29
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3060 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×D1827, C2×C5×C3⋊(ΓL(1,𝔽8)⋊D29), C5×D3×D609, …
maximal normal subgroup ofC2×C5×C3⋊(ΓL(1,𝔽8)⋊D29), C2×C3×C5×D609
maximal quotient ofC2×C5×D1827, C5×D3×D609, C2×C3×C5×D609, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 154);