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C5×AGL(1,𝔽5)2 #14522933

order2000
isoclinismisoclinic class of AGL(1,𝔽5)2
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C4

Aliases

direct productC5×AGL(1,𝔽5)2

Splittings

Fitting, socle, SylowC53 ⋊ C42
derivedC52 ⋊ C42×C5

Subgroups

subgroupG/H
center, hypercenterC5AGL(1,𝔽5)2
commutator, hypocenterC52C42×C5
FrattiniC1G
Fitting, socleC53C42
prime radicalC5×D52C22
cosocleD52C22×C5
LCSG ▷ C52
UCSC1 ◁ C5

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×AGL(1,ℤ/25), D5×AGL(1,𝔽5)2, C2×C5×AGL(1,𝔽5)2, …
maximal normal subgroup ofD5×AGL(1,𝔽5)2, C2×C5×AGL(1,𝔽5)2
maximal quotient ofAGL(1,𝔽5)×AGL(1,ℤ/25), C2×C5×AGL(1,𝔽5)2, AGL(1,𝔽5)2×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 896);