Finite Group Databasebeta

← Prev (#72258427) Next (#72258429) →

C4×#11717353 #72258428

order3200
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#11717353

Splittings

SylowC52 ⋊ C42×Q8

Subgroups

subgroupG/H
centerC2×C4C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C22×C42
FrattiniC22C22×D5⋊AGL(1,𝔽5)
FittingC42×C52C2×C4
socleC22×C52C23×C4
prime radical, cosocleC22×C5⋊D5C24
hypercenterC42D5⋊AGL(1,𝔽5)
hypocenterC52C42×Q8
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C42

1626 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 ofC4×#13107559
maximal normal subgroup ofC4×#13107559

GAP

Past the SmallGroups library coverage — no SmallGroups id.