Finite Group Databasebeta

← Prev (#72242519) Next (#72242521) →

C2×D5⋊#3993 #72242520

order3200
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5⋊#3993

Splittings

FittingC2×C52×C8 ⋊ C2×C4
SylowC52 ⋊ C22×#106

Subgroups

subgroupG/H
centerC22D5⋊(C4⋊AGL(1,𝔽5))
commutatorC4×C52C23×C4
FrattiniC4C22×D5⋊AGL(1,𝔽5)
FittingC2×C52×C8C2×C4
socleC22×C52C2×C4⋊C4
prime radicalC22×D52D4
cosocleC4×C5⋊D5C24
hypercenterC2×C8D5⋊AGL(1,𝔽5)
hypocenterC52C22×#106
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

1330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#106×D5⋊AGL(1,𝔽5), #72242587, #72242598
maximal normal subgroup of#106×D5⋊AGL(1,𝔽5), #72242587, #72242598

GAP

Past the SmallGroups library coverage — no SmallGroups id.