Finite Group Databasebeta

← Prev (#49178442) Next (#49178444) →

C5×C11⋊(#4296⋊C4) #49178443

order37620
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊(#4296⋊C4)
unambiguous semidirect product#4296⋊(C5×Dic11)

Splittings

derived, HallC11×C19 ⋊ C4×C5×C9
HallC5×C11×#4296 ⋊ C4
HallC5×Dic209 ⋊ C9
HallC11×#4296 ⋊ C4×C5
HallC5×C11×C19 ⋊ C4×C9
HallC5×#4296 ⋊ Dic11
HallDic209 ⋊ C5×C9
Hall#4296 ⋊ C5×Dic11
HallC5×C19 ⋊ C9×Dic11
HallC5×C11 ⋊ #4296⋊C4
SylowC19 ⋊ C5×C9×Dic11
SylowC11 ⋊ C5×#4296⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊AGL(1,𝔽19)
commutator, hypocenterC11×C19C4×C5×C9
FrattiniC2C5×C11⋊AGL(1,𝔽19)
Fitting, socleC2×C5×C11×C19C2×C9
prime radicalC2×C5×C11×C19⋊C3C2×C3
cosocleC2×C11×C19⋊C3C2×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4180

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 152);