Finite Group Databasebeta

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D5×#88907 #72247447

order4320
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C24

Aliases

direct productD5×#88907

Splittings

HallC24×D5 ⋊ 3−1+2
SylowC5 ⋊ C2×#88907

Subgroups

subgroupG/H
center, FrattiniC3C3×D5×C22⋊A4
commutator, socle, cosocleC24×C3×C5C2×C32
FittingC24×C32×C5C2×C3
prime radicalC24×C32×D5C3
hypercenterC32D5×C22⋊A4
hypocenterC24×C5C2×3−1+2
LCSG ▷ C24×C3×C5 ▷ C24×C5
UCSC1 ◁ C3 ◁ C32

1664 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 75 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) = 180

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×#13049240, AGL(1,𝔽5)×#88907, D5×#11724050
maximal normal subgroup ofD5×#13049240, AGL(1,𝔽5)×#88907, D5×#11724050

GAP

Past the SmallGroups library coverage — no SmallGroups id.