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C32×D1045 #34037909

order18810
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC32×D1045
unambiguous semidirect productC5⋊(C32×D209)
unambiguous semidirect productC11⋊(C32×D95)

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C2
derived, HallC5×C11×C19 ⋊ C2×C32
HallC32×C11×C19 ⋊ D5
HallC32×C5×C19 ⋊ D11
HallC32×C5×C11 ⋊ D19
HallC11×C19 ⋊ C32×D5
HallC32×C19 ⋊ D55
HallC32×C11 ⋊ D95
HallC5×C19 ⋊ C32×D11
HallC5×C11 ⋊ C32×D19
HallC32×C5 ⋊ D209
SylowC19 ⋊ C32×D55
SylowC11 ⋊ C32×D95
SylowC5 ⋊ C32×D209

Subgroups

subgroupG/H
center, hypercenterC32D1045
commutator, cosocle, hypocenterC5×C11×C19C2×C32
FrattiniC1G
Fitting, socleC32×C5×C11×C19C2
LCSG ▷ C5×C11×C19
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

4716 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×D19×D55, C32×D11×D95, C32×D5×D209, …
maximal normal subgroup ofC32×D19×D55, C32×D11×D95, C32×D5×D209, …
maximal quotient ofC32×Dic1045, C2×C32×D1045

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 102);