Finite Group Databasebeta

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C2×#72213584 #72258372

order12800
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#72213584

Splittings

FittingC2×C52×#127 ⋊ C2×C4
SylowC52 ⋊ C2×C4×#453

Subgroups

subgroupG/H
centerC22#72213578
commutatorC2×C4×C52C24×C4
FrattiniC2×C4C23×D5⋊AGL(1,𝔽5)
FittingC2×C52×#127C2×C4
socleC22×C52C4×#120
prime radicalC2×#72213351C2
cosocleC2×C4×C5⋊D5C25
hypercenterC2×#127D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×#453
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

27294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.