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D35×D87 #27131805

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

Aliases

direct productD35×D87

Splittings

Fitting, socle, derived, HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C2×D3
HallC3×C7×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C2×D7
HallC7×C29 ⋊ D3×D5
HallC5×C29 ⋊ D3×D7
HallC3×C5×C7 ⋊ C2×D29
HallC3×C29 ⋊ C2×D35
HallC5×C7 ⋊ C2×D87
SylowC29 ⋊ D3×D35
HallC3×C7 ⋊ D5×D29
HallC3×C5 ⋊ D7×D29
SylowC7 ⋊ D5×D87
SylowC5 ⋊ D7×D87
SylowC3 ⋊ D29×D35

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C7×C29C22
LCSG ▷ C3×C5×C7×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

855 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD35×D261, D87×C5⋊AGL(1,𝔽7), C3×D35×D87, …
maximal normal subgroup ofD87×C5⋊AGL(1,𝔽7), C3×D35×D87
maximal quotient ofD35×D261, C3×D35×D87, D87×D105, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 140);