Finite Group Databasebeta

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C2×#72221300 #72242686

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

Aliases

direct productC2×#72221300

Splittings

SylowC52 ⋊ C2×#2875

Subgroups

subgroupG/H
centerC2×C4C22×D5⋊AGL(1,𝔽5)
commutatorC2×C52C23×C42
FrattiniC4C23×D5⋊AGL(1,𝔽5)
FittingC2×C52×#41C2×C4
socleC22×C52C22×C42
prime radicalC2×#41×C5⋊D5C22
cosocleC4×C5⋊D5C25
hypercenterC2×#41D5⋊AGL(1,𝔽5)
hypocenterC52C2×#2875
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C2×C4 ◁ C2×#41

8284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.