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C2×C5×C29×D21 #27131820

order12180
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C22×C5×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C29×D21
unambiguous semidirect product(C2×C3)⋊(C5×D7×C29)
unambiguous semidirect product(C2×C7)⋊(C5×D3×C29)

Splittings

Fitting, socleC2×C3×C5×C7×C29 ⋊ C2
derived, HallC3×C7 ⋊ C22×C5×C29
HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C2×D3
HallC3×C7×C29 ⋊ C22×C5
HallC3×C5×C29 ⋊ C2×D7
HallC7×C29 ⋊ C2×C5×D3
HallC3×C5×C7 ⋊ C22×C29
HallC3×C29 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×D3×C29
HallC3×C5 ⋊ C2×D7×C29
SylowC7 ⋊ C2×C5×D3×C29
SylowC3 ⋊ C2×C5×D7×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C29D21
commutator, hypocenterC3×C7C22×C5×C29
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C29C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C5×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C29×D63, C2×C5×C29×C3⋊AGL(1,𝔽7), C5×D3×C29×D21, …
maximal normal subgroup ofC2×C5×C29×C3⋊AGL(1,𝔽7), C2×C3×C5×C29×D21
maximal quotient ofC2×C5×C29×D63, C5×D3×C29×D21, C2×C3×C5×C29×D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 155);