Finite Group Databasebeta

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C22×#13103905 #72253347

order6400
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#13103905

Splittings

SylowC52 ⋊ C22×C4×M16

Subgroups

subgroupG/H
centerC22×C4C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C23×C42
FrattiniC4C23×D5⋊AGL(1,𝔽5)
FittingC23×C4×C52C2×C4
socleC23×C52C2×C42
prime radicalC24×C5⋊D5C2×C4
cosocleC4×C5⋊D5C25
hypercenterC23×C4D5⋊AGL(1,𝔽5)
hypocenterC52C22×C4×M16
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C4 ◁ C23×C4

10900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

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

Relationships

maximal quotient ofC22×#72220669

GAP

Past the SmallGroups library coverage — no SmallGroups id.