Finite Group Databasebeta

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C5×#64870 #13100060

order1600
isoclinismisoclinic class of #64868
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#64870

Splittings

SylowC52 ⋊ #330

Subgroups

subgroupG/H
centerC22×C5C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C2×C4×C5
FrattiniC2×C4C2×C5×AGL(1,𝔽5)
FittingC52×C4⋊C4C4
socle, prime radicalC22×C52C22⋊C4
cosocleC4×Dic5C22×C5
hypercenterC5×C4⋊C4AGL(1,𝔽5)
hypocenterC5C5×#330
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C5×C4⋊C4

133 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 133 conjugacy classes of subgroups — too many to draw. Only its 44 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) = 320

Conjugacy classes & character table

145 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 2412);