Finite Group Databasebeta

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C22×#72220669 #72269148

order12800
automorphism?
homologyAbelianization (H1) = C22×C43 · Schur multiplier (H2) = C28×C42

Aliases

direct productC22×#72220669

Splittings

SylowC52 ⋊ C22×C4×#97

Subgroups

subgroupG/H
centerC23×C4C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C22×C43
FrattiniC2×C4C23×D5⋊AGL(1,𝔽5)
FittingC22×C42×C52C2×C4
socleC24×C52C2×C42
prime radicalC24×C5⋊D5C22×C4
cosocleC2×C4×C5⋊D5C25
hypercenterC22×C42D5⋊AGL(1,𝔽5)
hypocenterC52C22×C4×#97
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23×C4 ◁ C22×C42

31014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.