Finite Group Databasebeta

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C32×C29×D35 #32912541

order18270
automorphism?
homologyAbelianization (H1) = C2×C32×C29 · Schur multiplier (H2) = C3

Aliases

direct productC32×C29×D35
unambiguous semidirect productC5⋊(C32×D7×C29)

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C2
derived, HallC5×C7 ⋊ C2×C32×C29
HallC32×C7×C29 ⋊ D5
HallC32×C5×C29 ⋊ D7
HallC5×C7×C29 ⋊ C2×C32
HallC32×C5×C7 ⋊ C2×C29
HallC7×C29 ⋊ C32×D5
HallC5×C29 ⋊ C32×D7
HallC32×C7 ⋊ D5×C29
HallC32×C5 ⋊ D7×C29
SylowC7 ⋊ C32×D5×C29
SylowC5 ⋊ C32×D7×C29

Subgroups

subgroupG/H
center, hypercenterC32×C29D35
commutator, cosocle, hypocenterC5×C7C2×C32×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C2
LCSG ▷ C5×C7
UCSC1 ◁ C32×C29

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

4959 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×D29×D35, C32×D5×D7×C29, C32×D35⋊D29, …
maximal normal subgroup ofC32×D29×D35, C32×D5×D7×C29, C32×D35⋊D29, …
maximal quotient ofC32×C29×Dic35, C2×C32×C29×D35

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 79);