Finite Group Databasebeta

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C3×D3×D1015 #49141588

order36540
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D3×D1015
unambiguous semidirect product(C5×D3)⋊(C3×D203)
unambiguous semidirect product(D3×C29)⋊(C3×D35)

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C22
derivedC3×C5×C7×C29 ⋊ C22×C3
HallC32×C7×C29 ⋊ C2×D5
HallC32×C5×C29 ⋊ C2×D7
HallC5×C7×C29 ⋊ C2×C3×D3
HallC32×C5×C7 ⋊ C2×D29
HallC32×C29 ⋊ C2×D35
HallC7×C29 ⋊ C3×D3×D5
HallC5×C29 ⋊ C3×D3×D7
HallC32×C7 ⋊ C2×D145
HallC32×C5 ⋊ C2×D203
HallC5×C7 ⋊ C3×D3×D29
SylowC29 ⋊ C3×D3×D35
SylowC32 ⋊ C2×D1015
SylowC7 ⋊ C3×D3×D145
SylowC5 ⋊ C3×D3×D203

Subgroups

subgroupG/H
center, hypercenterC3D3×D1015
commutator, cosocle, hypocenterC3×C5×C7×C29C22×C3
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C3×C5×C7×C29
UCSC1 ◁ C3

176 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6090

Conjugacy classes & character table

4581 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 430);