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C72×AGL(1,𝔽13) #21439585

order7644
isoclinismisoclinic class of AGL(1,𝔽13)
automorphism?
homologyAbelianization (H1) = C3×C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC72×AGL(1,𝔽13)
unambiguous semidirect product#261⋊(C3×C72)

Splittings

Fitting, socle, HallC72×C13 ⋊ C3×C4
derived, SylowC13 ⋊ C3×C4×C72
HallC72×#261 ⋊ C3
HallC72×C13⋊C3 ⋊ C4
Hall#261 ⋊ C3×C72
HallC13⋊C3 ⋊ C4×C72

Subgroups

subgroupG/H
center, hypercenterC72AGL(1,𝔽13)
commutator, hypocenterC13C3×C4×C72
FrattiniC1G
Fitting, socleC72×C13C3×C4
LCSG ▷ C13
UCSC1 ◁ C72

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

637 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×ΓL(1,𝔽8)×AGL(1,𝔽13), #3861×AGL(1,𝔽13), #3862×AGL(1,𝔽13), …
maximal normal subgroup ofC7×ΓL(1,𝔽8)×AGL(1,𝔽13), #3861×AGL(1,𝔽13), #3862×AGL(1,𝔽13), …
maximal quotient ofC72×#261⋊C9, C3×C72×AGL(1,𝔽13), C72×C3⋊AGL(1,𝔽13), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 154);