Finite Group Databasebeta

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C5×#11717375 #72259192

order4000
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#11717375

Splittings

FittingC22×C53 ⋊ C2×C4
SylowC53 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C5C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C22×C4×C5
FrattiniC2C2×C5×D5⋊AGL(1,𝔽5)
FittingC22×C53C2×C4
socleC2×C53C22×C4
prime radicalC5×#87886C2
cosocleC2×C5⋊D5C23×C5
hypercenterC22×C5D5⋊AGL(1,𝔽5)
hypocenterC52C4×C5×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C5 ◁ C22×C5

536 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 80

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#11717375
maximal normal subgroup ofD5×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.