Finite Group Databasebeta

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C32×C7⋊#10596815 #49141544

order36540
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7⋊#10596815

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C4
derived, HallC5×C7×C29 ⋊ C32×C4
HallC32×C7×C29 ⋊ AGL(1,𝔽5)
HallC32×C5×C29 ⋊ Dic7
HallC32×C5×C7 ⋊ #1181
HallC32×C29 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C29 ⋊ C32×AGL(1,𝔽5)
HallC5×C29 ⋊ C32×Dic7
HallC32×C7 ⋊ #10596815
HallC32×C5 ⋊ C7⋊#1181
HallC5×C7 ⋊ C32×#1181
SylowC29 ⋊ C32×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C32×#10596815
SylowC5 ⋊ C32×C7⋊#1181

Subgroups

subgroupG/H
center, hypercenterC32C7⋊#10596815
commutator, hypocenterC5×C7×C29C32×C4
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC32×C7×D145C2
cosocleC7×D145C2×C32
LCSG ▷ C5×C7×C29
UCSC1 ◁ C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

2358 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 386);