Finite Group Databasebeta

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D5×#6911 #72247205

order2430
automorphism?
homologyAbelianization (H1) = C2×C33 · Schur multiplier (H2) = C34

Aliases

direct productD5×#6911

Splittings

Fitting, HallC5×#6911 ⋊ C2
SylowC5 ⋊ C2×#6911

Subgroups

subgroupG/H
centerC3C3×D5×H(3,𝔽3)
commutator, cosocleC32×C5C2×C33
FrattiniC32C33×D5
FittingC5×#6911C2
socleC3×C5C2×C3×H(3,𝔽3)
hypercenter#6911D5
hypocenterC5C2×#6911
LCSG ▷ C32×C5 ▷ C3×C5 ▷ C5
UCSC1 ◁ C3 ◁ C33 ◁ #6911

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 135

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#6911, D5×#10624749, D5×#92333, …
maximal normal subgroup ofAGL(1,𝔽5)×#6911, D5×#10624749, D5×#92333, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.