Finite Group Databasebeta

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C2×C3×C17×D165 #46778207

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

Aliases

direct productC2×C3×C17×D165
unambiguous semidirect product(C2×C3)⋊(C3×C17×D55)
unambiguous semidirect product(C2×C5)⋊(C3×C17×D33)
unambiguous semidirect product(C2×C11)⋊(C3×C17×D15)

Splittings

Fitting, socleC2×C32×C5×C11×C17 ⋊ C2
derivedC3×C5×C11 ⋊ C22×C3×C17
HallC32×C5×C11×C17 ⋊ C22
HallC32×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×C3×D3
HallC32×C5×C17 ⋊ C2×D11
HallC32×C5×C11 ⋊ C22×C17
HallC11×C17 ⋊ C2×C3×D15
HallC32×C17 ⋊ C2×D55
HallC32×C11 ⋊ C2×D5×C17
HallC5×C17 ⋊ C2×C3×D33
HallC5×C11 ⋊ C2×C3×D3×C17
HallC32×C5 ⋊ C2×C17×D11
SylowC11 ⋊ C2×C3×C17×D15
SylowC32 ⋊ C2×C17×D55
SylowC5 ⋊ C2×C3×C17×D33

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D165
commutator, cosocle, hypocenterC3×C5×C11C22×C3×C17
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C17C2
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C3×C17

176 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 11220

Conjugacy classes & character table

8568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 375);