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ΓL(1,𝔽16)×C181 #24925835

order10860
isoclinismisoclinic class of ΓL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C4×C181 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽16)×C181
unambiguous semidirect productC3⋊(AGL(1,𝔽5)×C181)

Splittings

Fitting, socle, HallC3×C5×C181 ⋊ C4
derived, HallC3×C5 ⋊ C4×C181
HallC5×C181 ⋊ Dic3
HallC3×C181 ⋊ AGL(1,𝔽5)
SylowC5 ⋊ Dic3×C181
SylowC3 ⋊ AGL(1,𝔽5)×C181

Subgroups

subgroupG/H
center, hypercenterC181ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C181
FrattiniC1G
Fitting, socleC3×C5×C181C4
prime radicalC3×D5×C181C2
cosocleC3×D5C2×C181
LCSG ▷ C3×C5
UCSC1 ◁ C181

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1629 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9⋊AGL(1,𝔽5)×C181, ΓL(1,𝔽16)×C181⋊C3, C3×ΓL(1,𝔽16)×C181, …
maximal normal subgroup ofΓL(1,𝔽16)×C181⋊C3, C3×ΓL(1,𝔽16)×C181
maximal quotient ofC9⋊AGL(1,𝔽5)×C181, C3×ΓL(1,𝔽16)×C181, C3⋊ΓL(1,𝔽16)×C181

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10860, 51);