Finite Group Databasebeta

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C5×#64899 #13100089

order1600
automorphism?
homologyAbelianization (H1) = C42×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#64899

Splittings

FittingC52×M16 ⋊ C4
SylowC52 ⋊ #343

Subgroups

subgroupG/H
centerC2×C5(C2×AGL(1,𝔽5))⋊C4
commutatorC22×C5C42×C5
FrattiniC2×C4C2×C5×AGL(1,𝔽5)
FittingC52×M16C4
socleC2×C52#95
prime radicalC22×C5×D5C2×C4
cosocleC2×C4×D5C22×C5
hypercenterC5×M16AGL(1,𝔽5)
hypocenterC5C5×#343
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×M16

206 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽5)×#100, C5×#10604863, C5×#10604003, …
maximal normal subgroup ofC5×AGL(1,𝔽5)×#100, C5×#10604863, C5×#10604003
maximal quotient of#72275776

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 2441);