Finite Group Databasebeta

← Prev (#72221613) Next (#72221615) →

C5×#10604618 #72221614

order3200
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#10604618

Splittings

FittingC52×#127 ⋊ C4
SylowC52 ⋊ #1884

Subgroups

subgroupG/H
centerC2×C5#65779
commutatorC2×C4×C5C22×C4×C5
FrattiniC2×C4C22×C5×AGL(1,𝔽5)
FittingC52×#127C4
socleC2×C52#386
prime radicalC5×#66050C2
cosocleC2×C4×D5C23×C5
hypercenterC5×#127AGL(1,𝔽5)
hypocenterC5C5×#1884
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#127

718 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72221622
maximal normal subgroup of#72221622

GAP

Past the SmallGroups library coverage — no SmallGroups id.