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C5×(C49⋊C3)⋊AGL(1,𝔽5) #28412925

order14700
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C49⋊C3)⋊AGL(1,𝔽5)
unambiguous semidirect product(C49⋊C3)⋊(C5×AGL(1,𝔽5))
unambiguous semidirect product(C49⋊AGL(1,𝔽5))⋊(C3×C5)
unambiguous semidirect product(C5×C49⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, HallC52×C49 ⋊ C3×C4
derivedC5×C49 ⋊ C3×C4×C5
HallC5×C49⋊AGL(1,𝔽5) ⋊ C3
HallC52×C49⋊C3 ⋊ C4
HallC49⋊C3 ⋊ C5×AGL(1,𝔽5)
SylowC49 ⋊ C3×C5×AGL(1,𝔽5)
SylowC52 ⋊ (C49⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC5(C49⋊C3)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C49C3×C4×C5
FrattiniC7C5×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
FittingC52×C49C3×C4
socleC52×C7ΓL(1,𝔽8)⋊C4
prime radicalC5×D5×C49⋊C3C2
cosocleD5×C49C2×C3×C5
LCSG ▷ C5×C49
UCSC1 ◁ C5

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

235 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 104);