Finite Group Databasebeta

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C3×D5×D161 #23751607

order9660
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×D161
unambiguous semidirect product(D5×C23)⋊(C3×D7)

Splittings

Fitting, socle, HallC3×C5×C7×C23 ⋊ C22
derived, HallC5×C7×C23 ⋊ C22×C3
HallC3×C7×C23 ⋊ C2×D5
HallC3×C5×C23 ⋊ C2×D7
HallC7×C23 ⋊ C2×C3×D5
HallC5×C23 ⋊ C2×C3×D7
HallC3×C5×C7 ⋊ C2×D23
HallC3×C23 ⋊ D5×D7
HallC5×C7 ⋊ C2×C3×D23
SylowC23 ⋊ C3×D5×D7
HallC3×C7 ⋊ D5×D23
HallC3×C5 ⋊ C2×D161
SylowC7 ⋊ C3×D5×D23
SylowC5 ⋊ C2×C3×D161

Subgroups

subgroupG/H
center, hypercenterC3D5×D161
commutator, cosocle, hypocenterC5×C7×C23C22×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C23C22
LCSG ▷ C5×C7×C23
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

984 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C23⋊(D7⋊C9), C9×D5×D161, C3×D5×ΓL(1,𝔽8)⋊D23, …
maximal normal subgroup ofD5×C23⋊(D7⋊C9), C9×D5×D161, C3×D5×ΓL(1,𝔽8)⋊D23, …
maximal quotient ofC9×D5×D161, C32×D5×D161, C3×D15×D161, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9660, 53);