Finite Group Databasebeta

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C2×C5×C7×D87 #27131821

order12180
isoclinismisoclinic class of D87
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D87
unambiguous semidirect product(C2×C3)⋊(C5×C7×D29)

Splittings

Fitting, socleC2×C3×C5×C7×C29 ⋊ C2
derived, HallC3×C29 ⋊ C22×C5×C7
HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C2×D3
HallC3×C7×C29 ⋊ C22×C5
HallC3×C5×C29 ⋊ C22×C7
HallC7×C29 ⋊ C2×C5×D3
HallC5×C29 ⋊ C2×D3×C7
HallC3×C5×C7 ⋊ C2×D29
SylowC29 ⋊ C2×C5×D3×C7
HallC3×C7 ⋊ C2×C5×D29
HallC3×C5 ⋊ C2×C7×D29
SylowC3 ⋊ C2×C5×C7×D29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D87
commutator, hypocenterC3×C29C22×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C29C2
LCSG ▷ C3×C29
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C7×D261, C2×C5×ΓL(1,𝔽8)×D87, C5×D3×C7×D87, …
maximal normal subgroup ofC2×C5×ΓL(1,𝔽8)×D87, C2×C3×C5×C7×D87
maximal quotient ofC2×C5×C7×D261, C5×D3×C7×D87, C2×C3×C5×C7×D87, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 156);