Finite Group Databasebeta

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C4×C5×C22⋊AGL(1,𝔽5) #13104523

order1600
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×C5×C22⋊AGL(1,𝔽5)

Splittings

FittingC22×C4×C52 ⋊ C4
SylowC52 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
centerC2×C4×C5C2×AGL(1,𝔽5)
commutatorC2×C5C2×C42×C5
FrattiniC22C22×C5×AGL(1,𝔽5)
FittingC22×C4×C52C4
socleC22×C52C22×C4
prime radicalC23×C5×D5C22
cosocleC22×D5C23×C5
hypercenterC22×C4×C5AGL(1,𝔽5)
hypocenterC5C4×C5×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5

543 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 543 conjugacy classes of subgroups — too many to draw. Only its 172 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

280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 6875);