Finite Group Databasebeta

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C17×D11×C3⋊D15 #46778173

order33660
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2×C3

Aliases

direct productC17×D11×C3⋊D15
unambiguous semidirect product(C3×D11)⋊(C17×D15)
unambiguous semidirect product(C5×D11)⋊(C17×C3⋊D3)

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C22
derived, HallC32×C5×C11 ⋊ C22×C17
HallC32×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×C3⋊D3
HallC32×C5×C17 ⋊ C2×D11
HallC11×C17 ⋊ C2×C3⋊D15
HallC32×C17 ⋊ D5×D11
HallC32×C11 ⋊ C2×D5×C17
HallC5×C17 ⋊ C3⋊D3×D11
HallC5×C11 ⋊ C2×C17×C3⋊D3
HallC32×C5 ⋊ C2×C17×D11
SylowC11 ⋊ C2×C17×C3⋊D15
SylowC32 ⋊ D5×C17×D11
SylowC5 ⋊ C17×C3⋊D3×D11

Subgroups

subgroupG/H
center, hypercenterC17D11×C3⋊D15
commutator, cosocle, hypocenterC32×C5×C11C22×C17
FrattiniC1G
Fitting, socleC32×C5×C11×C17C22
LCSG ▷ C32×C5×C11
UCSC1 ◁ C17

240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 8415

Conjugacy classes & character table

2856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 341);