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AGL(1,𝔽5)×C353 #20296558

order7060
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C353 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C353

Splittings

Fitting, socle, HallC5×C353 ⋊ C4
derived, SylowC5 ⋊ C4×C353

Subgroups

subgroupG/H
center, hypercenterC353AGL(1,𝔽5)
commutator, hypocenterC5C4×C353
FrattiniC1G
Fitting, socleC5×C353C4
LCSG ▷ C5
UCSC1 ◁ C353

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1765 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×AGL(1,𝔽5)×C353, ΓL(1,𝔽16)×C353, #1035×C353, …
maximal normal subgroup ofC3×AGL(1,𝔽5)×C353, C5×AGL(1,𝔽5)×C353
maximal quotient ofC3×AGL(1,𝔽5)×C353, ΓL(1,𝔽16)×C353, #1035×C353, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7060, 7);