Finite Group Databasebeta

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C2×#72213578 #72258324

order6400
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×#72213578

Splittings

FittingC22×C52×D4 ⋊ C2×C4
SylowC52 ⋊ C2×C4×#120

Subgroups

subgroupG/H
centerC23C22×D5⋊AGL(1,𝔽5)
commutatorC22×C52C24×C4
FrattiniC22C23×D5⋊AGL(1,𝔽5)
FittingC22×C52×D4C2×C4
socleC23×C52C23×C4
prime radicalC2×#13106387C2
cosocleC22×C5⋊D5C25
hypercenterC22×D4D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×#120
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×D4

19692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

Relationships

maximal quotient ofC2×#72213584

GAP

Past the SmallGroups library coverage — no SmallGroups id.