Finite Group Databasebeta

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C5×#64894 #13100084

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

Aliases

direct productC5×#64894

Splittings

FittingC2×C52×C8 ⋊ C4
SylowC52 ⋊ #344

Subgroups

subgroupG/H
centerC4×C5C22⋊AGL(1,𝔽5)
commutatorC22×C5C42×C5
FrattiniC2×C4C2×C5×AGL(1,𝔽5)
FittingC2×C52×C8C4
socleC2×C52#95
prime radicalC22×C5×D5C2×C4
cosocleC2×C4×D5C22×C5
hypercenterC2×C5×C8AGL(1,𝔽5)
hypocenterC5C5×#344
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×C8

191 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 191 conjugacy classes of subgroups — too many to draw. Only its 68 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, 2436);