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C49⋊C3×C11⋊AGL(1,𝔽5) #44568354

order32340
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC49⋊C3×C11⋊AGL(1,𝔽5)
unambiguous semidirect productC11⋊(AGL(1,𝔽5)×C49⋊C3)
unambiguous semidirect product(C49×C11⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, derived, HallC5×C11×C49 ⋊ C3×C4
HallC49×C11⋊AGL(1,𝔽5) ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C4
HallC11×C49⋊C3 ⋊ AGL(1,𝔽5)
HallC5×C49⋊C3 ⋊ Dic11
HallC11×C49 ⋊ C3×AGL(1,𝔽5)
HallC5×C49 ⋊ C3×Dic11
HallC5×C11 ⋊ C4×C49⋊C3
SylowC49 ⋊ C3×C11⋊AGL(1,𝔽5)
SylowC11 ⋊ AGL(1,𝔽5)×C49⋊C3
SylowC5 ⋊ Dic11×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC5×C11×C49C3×C4
FrattiniC7ΓL(1,𝔽8)×C11⋊AGL(1,𝔽5)
socleC5×C7×C11C4×ΓL(1,𝔽8)
prime radicalD5×C11×C49⋊C3C2
cosocleD5×C11×C49C2×C3
LCSG ▷ C5×C11×C49
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 56);