Finite Group Databasebeta

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C3×D5×C11×D51 #46778102

order33660
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×C11×D51
unambiguous semidirect product(C3×D5)⋊(C3×C11×D17)
unambiguous semidirect product(D5×C17)⋊(C3×D3×C11)

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C22
derivedC3×C5×C17 ⋊ C22×C3×C11
HallC32×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×C3×D3
HallC32×C5×C17 ⋊ C22×C11
HallC32×C5×C11 ⋊ C2×D17
HallC11×C17 ⋊ C3×D3×D5
HallC32×C17 ⋊ C2×D5×C11
HallC32×C11 ⋊ D5×D17
HallC5×C17 ⋊ C2×C3×D3×C11
HallC5×C11 ⋊ C2×C3×D51
HallC32×C5 ⋊ C2×C11×D17
SylowC17 ⋊ C3×D3×D5×C11
SylowC32 ⋊ D5×C11×D17
SylowC5 ⋊ C2×C3×C11×D51

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×D51
commutator, cosocle, hypocenterC3×C5×C17C22×C3×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C17C22
LCSG ▷ C3×C5×C17
UCSC1 ◁ C3×C11

176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 5610

Conjugacy classes & character table

3564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 270);