Finite Group Databasebeta

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C2×#72221487 #72242659

order6400
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×#72221487

Splittings

FittingC2×C42×C52 ⋊ C2×C4
SylowC52 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC22×C4C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C23×C42
FrattiniC22C23×D5⋊AGL(1,𝔽5)
FittingC2×C42×C52C2×C4
socleC23×C52C23×C4
prime radicalC23×D52C23
cosocleC22×C5⋊D5C25
hypercenterC2×C42D5⋊AGL(1,𝔽5)
hypocenterC52C2×C4×#117
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22×C4 ◁ C2×C42

10196 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.