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C11×C49⋊AGL(1,𝔽5) #24924708

order10780
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC5×C11×C49 ⋊ C4
derived, HallC5×C49 ⋊ C4×C11
HallC11×C49 ⋊ AGL(1,𝔽5)
HallC5×C11 ⋊ Dic49
SylowC49 ⋊ C11×AGL(1,𝔽5)
SylowC5 ⋊ C11×Dic49

Subgroups

subgroupG/H
center, hypercenterC11C49⋊AGL(1,𝔽5)
commutator, hypocenterC5×C49C4×C11
FrattiniC7C11×C7⋊AGL(1,𝔽5)
FittingC5×C11×C49C4
socleC5×C7×C11Dic7
prime radicalC7×D5×C11D7
cosocleD5×C49C2×C11
LCSG ▷ C5×C49
UCSC1 ◁ C11

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1111 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×(C49⋊C3)⋊AGL(1,𝔽5), C3×C11×C49⋊AGL(1,𝔽5), C11×C3⋊(C49⋊AGL(1,𝔽5))
maximal normal subgroup ofC11×(C49⋊C3)⋊AGL(1,𝔽5), C3×C11×C49⋊AGL(1,𝔽5)
maximal quotient ofC3×C11×C49⋊AGL(1,𝔽5), C11×C3⋊(C49⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 21);