Finite Group Databasebeta

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C2×C3×C7×D5×C29 #27131826

order12180
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D5×C29
unambiguous semidirect productC5⋊(C22×C3×C7×C29)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C7×C29)

Splittings

Fitting, socleC2×C3×C5×C7×C29 ⋊ C2
derived, SylowC5 ⋊ C22×C3×C7×C29
HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C22×C3
HallC3×C5×C29 ⋊ C22×C7
HallC5×C29 ⋊ C22×C3×C7
HallC3×C5×C7 ⋊ C22×C29
HallC5×C7 ⋊ C22×C3×C29
HallC3×C5 ⋊ C22×C7×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C29D5
commutator, hypocenterC5C22×C3×C7×C29
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C29C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C7×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4872 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D5×C29×C7⋊C9, C2×C7×C9×D5×C29, C2×C3×D5×ΓL(1,𝔽8)×C29, …
maximal normal subgroup ofC2×D5×C29×C7⋊C9, C2×C7×C9×D5×C29, C2×C3×D5×ΓL(1,𝔽8)×C29, …
maximal quotient ofC2×C7×C9×D5×C29, C3×D3×C7×D5×C29, C2×C32×C7×D5×C29, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 161);