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C2×C4×C22⋊AGL(1,𝔽5) #10617477

order640
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×C22⋊AGL(1,𝔽5)

Splittings

FittingC23×C4×C5 ⋊ C4
SylowC5 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×AGL(1,𝔽5)
commutatorC2×C5C22×C42
FrattiniC22C23×AGL(1,𝔽5)
FittingC23×C4×C5C4
socleC23×C5C22×C4
prime radicalC24×D5C22
cosocleC22×D5C24
hypercenterC23×C4AGL(1,𝔽5)
hypocenterC5C2×C4×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C23×C4

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13015527, #13015539, C2×#10598559, …
maximal normal subgroup of#13015527, #13015539, C2×#10598559, …
maximal quotient ofC2×C4×(C2×AGL(1,𝔽5))⋊C4, C42×C22⋊AGL(1,𝔽5), C2×#10604909, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 19559);