Finite Group Databasebeta

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D3×C11⋊C5×D51 #46778015

order33660
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×C11⋊C5×D51
unambiguous semidirect product(C3×D3)⋊(D17×C11⋊C5)
unambiguous semidirect product(D3×C17)⋊(D3×C11⋊C5)
unambiguous semidirect product(D3×C11×D51)⋊C5

Splittings

Fitting, socle, derived, HallC32×C11×C17 ⋊ C22×C5
HallC32×C17×C11⋊C5 ⋊ C22
HallD3×C11×D51 ⋊ C5
HallC17×C11⋊C5 ⋊ D32
HallC32×C11⋊C5 ⋊ C2×D17
HallC11×C17 ⋊ C5×D32
HallC32×C17 ⋊ C22×C11⋊C5
HallC32×C11 ⋊ C2×C5×D17
SylowC17 ⋊ D32×C11⋊C5
SylowC11 ⋊ C5×D3×D51
SylowC32 ⋊ C2×D17×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C11×C17C22×C5
LCSG ▷ C32×C11×C17
UCSC1

176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 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) = 1122

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 183);