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C32×C29×C7⋊AGL(1,𝔽5) #49141542

order36540
automorphism?
homologyAbelianization (H1) = C32×C4×C29 · Schur multiplier (H2) = C3

Aliases

direct productC32×C29×C7⋊AGL(1,𝔽5)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC32×C29C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C32×C4×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C4
prime radicalC32×C7×D5×C29C2
cosocleC7×D5C2×C32×C29
LCSG ▷ C5×C7
UCSC1 ◁ C32×C29

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9135

Conjugacy classes & character table

4437 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 384);