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C32×C11⋊(C19⋊AGL(1,𝔽5)) #49178661

order37620
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11⋊(C19⋊AGL(1,𝔽5))
unambiguous semidirect productC11⋊(C32×C19⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC32×C5×C11×C19 ⋊ C4
derived, HallC5×C11×C19 ⋊ C32×C4
HallC32×C11×C19 ⋊ AGL(1,𝔽5)
HallC32×C5×C19 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic19
HallC11×C19 ⋊ C32×AGL(1,𝔽5)
HallC32×C19 ⋊ C11⋊AGL(1,𝔽5)
HallC32×C11 ⋊ C19⋊AGL(1,𝔽5)
HallC5×C19 ⋊ C32×Dic11
HallC5×C11 ⋊ C32×Dic19
HallC32×C5 ⋊ Dic209
SylowC19 ⋊ C32×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ C32×C19⋊AGL(1,𝔽5)
SylowC5 ⋊ C32×Dic209

Subgroups

subgroupG/H
center, hypercenterC32C11⋊(C19⋊AGL(1,𝔽5))
commutator, hypocenterC5×C11×C19C32×C4
FrattiniC1G
Fitting, socleC32×C5×C11×C19C4
prime radicalC32×D5×C11×C19C2
cosocleD5×C11×C19C2×C32
LCSG ▷ C5×C11×C19
UCSC1 ◁ C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

3789 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 370);