Finite Group Databasebeta

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C22×C4×D5⋊AGL(1,𝔽5) #72221164

order3200
isoclinismisoclinic class of D5⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×C4×D5⋊AGL(1,𝔽5)

Splittings

FittingC22×C4×C52 ⋊ C2×C4
derived, SylowC52 ⋊ C23×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4D5⋊AGL(1,𝔽5)
commutator, hypocenterC52C23×C42
FrattiniC2C23×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC23×C52C22×C4
prime radicalC23×D52C22
cosocleC2×C5⋊D5C25
LCSG ▷ C52
UCSC1 ◁ C22×C4

6498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C4×#11717363, C2×#72221487, C22×#13107568, …
maximal normal subgroup ofC2×C4×#11717363, C2×#72221487, C22×#13107568, …
maximal quotient of#72221166, C2×C4×#11717363, C2×#72220832, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.