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C23×C4×AGL(1,𝔽5) #10619396

order640
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC23×C4×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C22×C42)

Splittings

FittingC23×C4×C5 ⋊ C4
derived, SylowC5 ⋊ C23×C42

Subgroups

subgroupG/H
center, hypercenterC23×C4AGL(1,𝔽5)
commutator, hypocenterC5C23×C42
FrattiniC2C24×AGL(1,𝔽5)
FittingC23×C4×C5C4
socleC24×C5C2×C4
prime radicalC24×D5C22
cosocleC2×D5C25
LCSG ▷ C5
UCSC1 ◁ C23×C4

3000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×AGL(1,𝔽5))⋊#95, #13021631, #13021655, …
maximal normal subgroup of(C2×AGL(1,𝔽5))⋊#95, #13021631, #13021655, …
maximal quotient ofC22×C42×AGL(1,𝔽5), C23×(C2×AGL(1,𝔽5))⋊C4, C22×#65686, …
automorphism group ofC5×C8×D5, C5×#676, C3×D5×C16, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 21478);