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C37×C11⋊AGL(1,𝔽5) #22550792

order8140
isoclinismisoclinic class of C11⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C37 · Schur multiplier (H2) = C1

Aliases

direct productC37×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(AGL(1,𝔽5)×C37)

Splittings

Fitting, socle, HallC5×C11×C37 ⋊ C4
derived, HallC5×C11 ⋊ C4×C37
HallC11×C37 ⋊ AGL(1,𝔽5)
HallC5×C37 ⋊ Dic11
SylowC11 ⋊ AGL(1,𝔽5)×C37
SylowC5 ⋊ C37×Dic11

Subgroups

subgroupG/H
center, hypercenterC37C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C4×C37
FrattiniC1G
Fitting, socleC5×C11×C37C4
LCSG ▷ C5×C11
UCSC1 ◁ C37

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

925 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC37⋊C3×C11⋊AGL(1,𝔽5), C3×C37×C11⋊AGL(1,𝔽5), C37×C3⋊(C11⋊AGL(1,𝔽5))
maximal normal subgroup ofC37⋊C3×C11⋊AGL(1,𝔽5), C3×C37×C11⋊AGL(1,𝔽5)
maximal quotient ofC3×C37×C11⋊AGL(1,𝔽5), C37×C3⋊(C11⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8140, 28);