Finite Group Databasebeta

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C32×D1105 #34091073

order19890
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC32×D1105
unambiguous semidirect productC5⋊(C32×D221)
unambiguous semidirect productC17⋊(C32×D65)

Splittings

Fitting, socle, HallC32×C5×C13×C17 ⋊ C2
derived, HallC5×C13×C17 ⋊ C2×C32
HallC32×C13×C17 ⋊ D5
HallC32×C5×C17 ⋊ D13
HallC32×C5×C13 ⋊ D17
HallC13×C17 ⋊ C32×D5
HallC32×C17 ⋊ D65
HallC32×C13 ⋊ D85
HallC5×C17 ⋊ C32×D13
HallC5×C13 ⋊ C32×D17
HallC32×C5 ⋊ D221
SylowC17 ⋊ C32×D65
SylowC13 ⋊ C32×D85
SylowC5 ⋊ C32×D221

Subgroups

subgroupG/H
center, hypercenterC32D1105
commutator, cosocle, hypocenterC5×C13×C17C2×C32
FrattiniC1G
Fitting, socleC32×C5×C13×C17C2
LCSG ▷ C5×C13×C17
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9945

Conjugacy classes & character table

4986 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19890, 58);