Finite Group Databasebeta

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C32×D665 #26046233

order11970
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC32×D665
unambiguous semidirect productC5⋊(C32×D133)

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C2
derived, HallC5×C7×C19 ⋊ C2×C32
HallC32×C7×C19 ⋊ D5
HallC32×C5×C19 ⋊ D7
HallC32×C5×C7 ⋊ D19
HallC32×C19 ⋊ D35
HallC7×C19 ⋊ C32×D5
HallC5×C19 ⋊ C32×D7
HallC32×C7 ⋊ D95
HallC32×C5 ⋊ D133
HallC5×C7 ⋊ C32×D19
SylowC19 ⋊ C32×D35
SylowC7 ⋊ C32×D95
SylowC5 ⋊ C32×D133

Subgroups

subgroupG/H
center, hypercenterC32D665
commutator, cosocle, hypocenterC5×C7×C19C2×C32
FrattiniC1G
Fitting, socleC32×C5×C7×C19C2
LCSG ▷ C5×C7×C19
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3006 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×D19×D35, C32×D7×D95, C32×D5×D133, …
maximal normal subgroup ofC32×D19×D35, C32×D7×D95, C32×D5×D133, …
maximal quotient ofC32×Dic665, C2×C32×D665

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 162);