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C2×D3045 #27131815

order12180
automorphismAut(G) order 8184960
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD6090
direct productC2×D3045
unambiguous semidirect product(C2×C3)⋊D1015
unambiguous semidirect product(C2×C5)⋊D609
unambiguous semidirect product(C2×C7)⋊D435
unambiguous semidirect product(C2×C29)⋊D105

Splittings

Fitting, socleC2×C3×C5×C7×C29 ⋊ C2
derived, HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C2×D3
HallC3×C7×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C2×D7
HallC7×C29 ⋊ C2×D15
HallC5×C29 ⋊ C2×D21
HallC3×C5×C7 ⋊ C2×D29
HallC3×C29 ⋊ C2×D35
HallC5×C7 ⋊ C2×D87
SylowC29 ⋊ C2×D105
HallC3×C7 ⋊ C2×D145
HallC3×C5 ⋊ C2×D203
SylowC7 ⋊ C2×D435
SylowC5 ⋊ C2×D609
SylowC3 ⋊ C2×D1015

Subgroups

subgroupG/H
center, hypercenterC2D3045
commutator, hypocenterC3×C5×C7×C29C22
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C29C2
LCSG ▷ C3×C5×C7×C29
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3048 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×D9135, C2×C3⋊(C5⋊(ΓL(1,𝔽8)⋊D29)), D3×D3045, …
maximal normal subgroup ofC2×C3⋊(C5⋊(ΓL(1,𝔽8)⋊D29)), C2×C3×D3045, D12180
maximal quotient ofC2×D9135, D3×D3045, C2×C3×D3045, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 150);