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D7×C29×D15 #27131792

order12180
automorphism?
homologyAbelianization (H1) = C22×C29 · Schur multiplier (H2) = C2

Aliases

direct productD7×C29×D15
unambiguous semidirect product(C3×D7)⋊(D5×C29)
unambiguous semidirect product(C5×D7)⋊(D3×C29)

Splittings

Fitting, socle, HallC3×C5×C7×C29 ⋊ C22
derived, HallC3×C5×C7 ⋊ C22×C29
HallC5×C7×C29 ⋊ C2×D3
HallC3×C7×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C2×D7
HallC7×C29 ⋊ C2×D15
HallC5×C29 ⋊ D3×D7
HallC3×C29 ⋊ D5×D7
HallC5×C7 ⋊ C2×D3×C29
HallC3×C7 ⋊ C2×D5×C29
HallC3×C5 ⋊ C2×D7×C29
SylowC7 ⋊ C2×C29×D15
SylowC5 ⋊ D3×D7×C29
SylowC3 ⋊ D5×D7×C29

Subgroups

subgroupG/H
center, hypercenterC29D7×D15
commutator, hypocenterC3×C5×C7C22×C29
FrattiniC1G
Fitting, socleC3×C5×C7×C29C22
LCSG ▷ C3×C5×C7
UCSC1 ◁ C29

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1305 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD7×C29×D45, C29×D15×AGL(1,𝔽7), C3×D7×C29×D15, …
maximal normal subgroup ofC29×D15×AGL(1,𝔽7), C3×D7×C29×D15
maximal quotient ofD7×C29×D45, C3×D7×C29×D15, C29×D21⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 127);