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C5×C49×ΓL(1,𝔽16) #28412977

order14700
isoclinismisoclinic class of ΓL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C4×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC5×C49×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C5×AGL(1,𝔽5)×C49)

Splittings

Fitting, HallC3×C52×C49 ⋊ C4
derivedC3×C5 ⋊ C4×C5×C49
HallC52×C49 ⋊ Dic3
HallC3×C49 ⋊ C5×AGL(1,𝔽5)
HallC3×C52 ⋊ C4×C49
SylowC52 ⋊ Dic3×C49
SylowC3 ⋊ C5×AGL(1,𝔽5)×C49

Subgroups

subgroupG/H
center, hypercenterC5×C49ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C5×C49
FrattiniC7C5×C7×ΓL(1,𝔽16)
FittingC3×C52×C49C4
socleC3×C52×C7C4×C7
prime radicalC3×C5×C7×D5C2×C7
cosocleC3×C7×D5C2×C5×C7
LCSG ▷ C3×C5
UCSC1 ◁ C5×C49

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2205 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14700, 156);