Finite Group Databasebeta

← Prev (#72242639) Next (#72242641) →

C2×#72220669 #72242640

order6400
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C24×C42

Aliases

direct productC2×#72220669

Splittings

SylowC52 ⋊ C2×C4×#97

Subgroups

subgroupG/H
centerC22×C4C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C2×C43
FrattiniC2×C4C22×D5⋊AGL(1,𝔽5)
FittingC2×C42×C52C2×C4
socleC23×C52C2×C42
prime radicalC23×C5⋊D5C22×C4
cosocleC2×C4×C5⋊D5C24
hypercenterC2×C42D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×#97
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C4 ◁ C2×C42

4852 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×#72220669
maximal normal subgroup ofC22×#72220669
maximal quotient ofC22×#72220669

GAP

Past the SmallGroups library coverage — no SmallGroups id.