Finite Group Databasebeta

← Prev (#72242532) Next (#72242534) →

C2×#72220867 #72242533

order6400
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#72220867

Splittings

FittingC2×C52×D8 ⋊ C2×C4
SylowC52 ⋊ C2×C4×#135

Subgroups

subgroupG/H
centerC22D4×D5⋊AGL(1,𝔽5)
commutatorC4×C52C24×C4
FrattiniC4C23×D5⋊AGL(1,𝔽5)
FittingC2×C52×D8C2×C4
socleC22×C52C2×C4×D4
prime radicalC2×#13105821C2
cosocleC4×C5⋊D5C25
hypercenterC2×D8D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×#135
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

6404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72269234
maximal normal subgroup of#72269234

GAP

Past the SmallGroups library coverage — no SmallGroups id.