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C5×#65739 #13104499

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

Aliases

direct productC5×#65739

Splittings

FittingC52×Q16 ⋊ C4
SylowC52 ⋊ #441

Subgroups

subgroupG/H
centerC2×C5D4×AGL(1,𝔽5)
commutatorC4×C5C22×C4×C5
FrattiniC4C22×C5×AGL(1,𝔽5)
FittingC52×Q16C4
socleC2×C52C4×D4
prime radicalC2×C5×D5C2×D4
cosocleC4×D5C23×C5
hypercenterC5×Q16AGL(1,𝔽5)
hypocenterC5C5×#441
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×Q16

225 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 225 conjugacy classes of subgroups — too many to draw. Only its 84 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, 6851);