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AGL(1,𝔽5)×C421 #22554545

order8420
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C421 · Schur multiplier (H2) = C1

Aliases

direct productAGL(1,𝔽5)×C421

Splittings

Fitting, socle, HallC5×C421 ⋊ C4
derived, SylowC5 ⋊ C4×C421

Subgroups

subgroupG/H
center, hypercenterC421AGL(1,𝔽5)
commutator, hypocenterC5C4×C421
FrattiniC1G
Fitting, socleC5×C421C4
LCSG ▷ C5
UCSC1 ◁ C421

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2105 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofAGL(1,𝔽5)×C421⋊C3, C3×AGL(1,𝔽5)×C421, ΓL(1,𝔽16)×C421
maximal normal subgroup ofAGL(1,𝔽5)×C421⋊C3, C3×AGL(1,𝔽5)×C421
maximal quotient ofC3×AGL(1,𝔽5)×C421, ΓL(1,𝔽16)×C421

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8420, 12);