Finite Group Databasebeta

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C32×C19⋊(Dic11⋊C5) #49178451

order37620
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C19⋊(Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C32×Dic19)
unambiguous semidirect product(C32×Dic209)⋊C5

Splittings

derived, HallC11×C19 ⋊ C32×C4×C5
HallC32×C19×C11⋊C5 ⋊ C4
HallC32×Dic209 ⋊ C5
HallC32×C11×C19 ⋊ C4×C5
HallC19×C11⋊C5 ⋊ C32×C4
HallDic209 ⋊ C32×C5
HallC32×C11⋊C5 ⋊ Dic19
HallC32×C19 ⋊ Dic11⋊C5
HallC32×C11 ⋊ C5×Dic19
HallC11⋊C5 ⋊ C32×Dic19
SylowC19 ⋊ C32×Dic11⋊C5
SylowC11 ⋊ C32×C5×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C32C19⋊AGL(1,𝔽11)
commutator, hypocenterC11×C19C32×C4×C5
FrattiniC2C32×C19⋊AGL(1,𝔽11)
Fitting, socleC2×C32×C11×C19C2×C5
prime radicalC2×C32×C19×C11⋊C5C2
cosocleC2×C11×C19C2×C32×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C32

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7524

Conjugacy classes & character table

1332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 160);