Finite Group Databasebeta

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C5×#65794 #13104555

order1600
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#65794

Splittings

FittingC52×#41 ⋊ C4
SylowC52 ⋊ #416

Subgroups

subgroupG/H
centerC4×C5C22⋊AGL(1,𝔽5)
commutatorC4×C5C22×C4×C5
FrattiniC4C22×C5×AGL(1,𝔽5)
FittingC52×#41C4
socleC2×C52C2×C22⋊C4
prime radicalC5×D5×#41C2
cosocleC4×D5C23×C5
hypercenterC5×#41AGL(1,𝔽5)
hypocenterC5C5×#416
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C5×#41

336 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 100 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

190 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 6907);