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C61×AGL(1,𝔽13) #23748918

order9516
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C1

Aliases

direct productC61×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C61)

Splittings

Fitting, socle, HallC13×C61 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C61
Hall#261×C61 ⋊ C3
HallC13⋊C3×C61 ⋊ C4
Hall#261 ⋊ C3×C61
HallC13⋊C3 ⋊ C4×C61

Subgroups

subgroupG/H
center, hypercenterC61AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C61
FrattiniC1G
Fitting, socleC13×C61C3×C4
prime radicalC61×D13⋊C3C2
cosocleD13C2×C3×C61
LCSG ▷ C13
UCSC1 ◁ C61

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

793 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽13)×C61⋊C3, C3×C61×AGL(1,𝔽13), C61×C3⋊AGL(1,𝔽13)
maximal normal subgroup ofAGL(1,𝔽13)×C61⋊C3, C3×C61×AGL(1,𝔽13)
maximal quotient ofC61×#261⋊C9, C3×C61×AGL(1,𝔽13), C61×C3⋊AGL(1,𝔽13)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9516, 27);