Finite Group Databasebeta

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D3×C7×D5×C29 #27131796

order12180
automorphism?
homologyAbelianization (H1) = C22×C7×C29 · Schur multiplier (H2) = C2

Aliases

direct productD3×C7×D5×C29
unambiguous semidirect product(C5×D3)⋊(C2×C7×C29)
unambiguous semidirect product(C3×D5)⋊(C2×C7×C29)
unambiguous semidirect productD15⋊(C2×C7×C29)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7×C29D3×D5
commutator, hypocenterC3×C5C22×C7×C29
FrattiniC1G
Fitting, socleC3×C5×C7×C29C22
LCSG ▷ C3×C5
UCSC1 ◁ C7×C29

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2436 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D5×D9×C29, D3×D5×ΓL(1,𝔽8)×C29, C3×D3×C7×D5×C29, …
maximal normal subgroup ofD3×D5×ΓL(1,𝔽8)×C29, C3×D3×C7×D5×C29
maximal quotient ofC7×D5×D9×C29, C3×D3×C7×D5×C29, D3×C7×C29×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 131);