Finite Group Databasebeta

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C2×C3×D1015 #27131823

order12180
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D1015
unambiguous semidirect product(C2×C5)⋊(C3×D203)
unambiguous semidirect product(C2×C29)⋊(C3×D35)

Splittings

Fitting, socleC2×C3×C5×C7×C29 ⋊ C2
derived, HallC5×C7×C29 ⋊ C22×C3
HallC3×C5×C7×C29 ⋊ C22
HallC3×C7×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C2×D7
HallC7×C29 ⋊ C2×C3×D5
HallC5×C29 ⋊ C2×C3×D7
HallC3×C5×C7 ⋊ C2×D29
HallC3×C29 ⋊ C2×D35
HallC5×C7 ⋊ C2×C3×D29
SylowC29 ⋊ C2×C3×D35
HallC3×C7 ⋊ C2×D145
HallC3×C5 ⋊ C2×D203
SylowC7 ⋊ C2×C3×D145
SylowC5 ⋊ C2×C3×D203

Subgroups

subgroupG/H
center, hypercenterC2×C3D1015
commutator, hypocenterC5×C7×C29C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C29C2
LCSG ▷ C5×C7×C29
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3054 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊(C29⋊(D7⋊C9)), C2×C9×D1015, C2×C3×C5⋊(ΓL(1,𝔽8)⋊D29), …
maximal normal subgroup ofC2×C5⋊(C29⋊(D7⋊C9)), C2×C9×D1015, C2×C3×C5⋊(ΓL(1,𝔽8)⋊D29), …
maximal quotient ofC2×C9×D1015, C3×D3×D1015, C2×C32×D1015, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 158);