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C5×C31×ΓL(1,𝔽16) #22604903

order9300
isoclinismisoclinic class of ΓL(1,𝔽16)
automorphism?
homologyAbelianization (H1) = C4×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC5×C31×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C5×AGL(1,𝔽5)×C31)

Splittings

Fitting, socle, HallC3×C52×C31 ⋊ C4
derivedC3×C5 ⋊ C4×C5×C31
HallC52×C31 ⋊ Dic3
HallC3×C31 ⋊ C5×AGL(1,𝔽5)
HallC3×C52 ⋊ C4×C31
SylowC52 ⋊ Dic3×C31
SylowC3 ⋊ C5×AGL(1,𝔽5)×C31

Subgroups

subgroupG/H
center, hypercenterC5×C31ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C5×C31
FrattiniC1G
Fitting, socleC3×C52×C31C4
LCSG ▷ C3×C5
UCSC1 ◁ C5×C31

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1395 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C31×C9⋊AGL(1,𝔽5), C5×ΓL(1,𝔽16)×C31⋊C3, C3×C5×C31×ΓL(1,𝔽16), …
maximal normal subgroup ofC5×ΓL(1,𝔽16)×C31⋊C3, C3×C5×C31×ΓL(1,𝔽16)
maximal quotient ofC5×C31×C9⋊AGL(1,𝔽5), C3×C5×C31×ΓL(1,𝔽16), C5×C31×C3⋊ΓL(1,𝔽16)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 177);