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C52×(C49⋊C3)⋊C4 #28412865

order14700
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC52×(C49⋊C3)⋊C4
unambiguous semidirect product(C49⋊C3)⋊(C4×C52)
unambiguous semidirect productDic49⋊(C3×C52)
unambiguous semidirect product(C5×Dic49)⋊(C3×C5)

Splittings

derived, SylowC49 ⋊ C3×C4×C52
HallC52×Dic49 ⋊ C3
HallC52×C49⋊C3 ⋊ C4
HallC52×C49 ⋊ C3×C4
HallDic49 ⋊ C3×C52
HallC49⋊C3 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC2×C52D49⋊C3
commutator, hypocenterC49C3×C4×C52
FrattiniC2×C7C52×AGL(1,𝔽7)
FittingC2×C52×C49C2×C3
socleC2×C52×C7AGL(1,𝔽7)
prime radicalC2×C52×C49⋊C3C2
cosocleC2×C49C2×C3×C52
LCSG ▷ C49
UCSC1 ◁ C2×C52

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

700 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 44);