Finite Group Databasebeta

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C2×D5×#3811 #72229902

order2880
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×D5×#3811

Splittings

FittingC23×C32×C5 ⋊ C23
HallC32×C5 ⋊ C23×D4
SylowC32 ⋊ C22×D4×D5
SylowC5 ⋊ C22×#3811

Subgroups

subgroupG/H
centerC22C2×D32×D5
commutator, cosocleC2×C32×C5C25
FrattiniC2C22×D32×D5
FittingC23×C32×C5C23
socleC22×C32×C5C24
hypercenterC23D32×D5
hypocenterC32×C5C23×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

6196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×AGL(1,𝔽5)×#3811, C2×C5⋊D5×#3811, D5×#10596675, …
maximal normal subgroup ofC2×AGL(1,𝔽5)×#3811, D5×#10596675, #72260246
maximal quotient ofD5×#10595100, C2×C5⋊D5×#3811

GAP

Past the SmallGroups library coverage — no SmallGroups id.