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C5×C13×C7⋊AGL(1,𝔽5) #22603271

order9100
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×C7⋊AGL(1,𝔽5)
unambiguous semidirect productC7⋊(C5×C13×AGL(1,𝔽5))

Splittings

Fitting, socle, HallC52×C7×C13 ⋊ C4
derivedC5×C7 ⋊ C4×C5×C13
HallC52×C13 ⋊ Dic7
HallC52×C7 ⋊ C4×C13
HallC7×C13 ⋊ C5×AGL(1,𝔽5)
SylowC52 ⋊ C13×Dic7
SylowC7 ⋊ C5×C13×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC5×C13C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C5×C13
FrattiniC1G
Fitting, socleC52×C7×C13C4
LCSG ▷ C5×C7
UCSC1 ◁ C5×C13

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1105 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C5×#19129733, C5×#19129734, …
maximal normal subgroup ofC5×C13×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C5×#19129733, C5×#19129734, …
maximal quotient ofC3×C5×C13×C7⋊AGL(1,𝔽5), C5×C13×C3⋊(C7⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9100, 56);