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AGL(1,𝔽5)×#1043 #14522934

order2000
isoclinismisoclinic class of AGL(1,𝔽5)×#1043
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C4

Aliases

direct productAGL(1,𝔽5)×#1043

Splittings

Fitting, socle, derived, SylowC53 ⋊ C42

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC53C42
prime radical, cosocleD5×C5⋊D5C22
LCSG ▷ C53
UCSC1

276 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 100

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×D5⋊AGL(1,𝔽5), C2×AGL(1,𝔽5)×#1043, C3×AGL(1,𝔽5)×#1043, …
maximal normal subgroup ofAGL(1,𝔽5)×D5⋊AGL(1,𝔽5), C2×AGL(1,𝔽5)×#1043, C3×AGL(1,𝔽5)×#1043
maximal quotient ofC2×AGL(1,𝔽5)×#1043, C3×AGL(1,𝔽5)×#1043, ΓL(1,𝔽16)×#1043, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 897);