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ΓL(1,𝔽16)×C151 #22583705

order9060
isoclinismisoclinic class of ΓL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C4×C151 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽16)×C151
unambiguous semidirect productC3⋊(AGL(1,𝔽5)×C151)

Splittings

Fitting, socle, HallC3×C5×C151 ⋊ C4
derived, HallC3×C5 ⋊ C4×C151
HallC5×C151 ⋊ Dic3
HallC3×C151 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic3×C151
SylowC3 ⋊ AGL(1,𝔽5)×C151

Subgroups

subgroupG/H
center, hypercenterC151ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C151
FrattiniC1G
Fitting, socleC3×C5×C151C4
LCSG ▷ C3×C5
UCSC1 ◁ C151

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1359 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC151×C9⋊AGL(1,𝔽5), ΓL(1,𝔽16)×C151⋊C3, C3×ΓL(1,𝔽16)×C151, …
maximal normal subgroup ofΓL(1,𝔽16)×C151⋊C3, C3×ΓL(1,𝔽16)×C151
maximal quotient ofC151×C9⋊AGL(1,𝔽5), C3×ΓL(1,𝔽16)×C151, C151×C3⋊ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9060, 39);