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AGL(1,𝔽5)×C331 #20268792

order6620
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C331 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C331

Splittings

Fitting, socle, HallC5×C331 ⋊ C4
derived, SylowC5 ⋊ C4×C331

Subgroups

subgroupG/H
center, hypercenterC331AGL(1,𝔽5)
commutator, hypocenterC5C4×C331
FrattiniC1G
Fitting, socleC5×C331C4
LCSG ▷ C5
UCSC1 ◁ C331

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1655 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C331⋊C3, C3×AGL(1,𝔽5)×C331, ΓL(1,𝔽16)×C331, …
maximal normal subgroup ofAGL(1,𝔽5)×C331⋊C3, C3×AGL(1,𝔽5)×C331, AGL(1,𝔽5)×C331⋊C5, …
maximal quotient ofC3×AGL(1,𝔽5)×C331, ΓL(1,𝔽16)×C331, #1035×C331, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6620, 10);