Finite Group Databasebeta

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C22×#13107568 #72242703

order6400
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×#13107568

Splittings

FittingC22×C52×D4 ⋊ C2×C4
SylowC52 ⋊ C22×C4×#41

Subgroups

subgroupG/H
centerC23C22×D5⋊AGL(1,𝔽5)
commutatorC2×C52C25×C4
FrattiniC2C24×D5⋊AGL(1,𝔽5)
FittingC22×C52×D4C2×C4
socleC23×C52C23×C4
prime radicalC22×#11717477C2
cosocleC2×C5⋊D5C26
hypercenterC22×D4D5⋊AGL(1,𝔽5)
hypocenterC52C22×C4×#41
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×D4

28284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.