Finite Group Databasebeta

← Prev (#72222995) Next (#72222997) →

C22×D5⋊(C4⋊AGL(1,𝔽5)) #72222996

order3200
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×D5⋊(C4⋊AGL(1,𝔽5))

Splittings

FittingC22×C4×C52 ⋊ C2×C4
SylowC52 ⋊ C23×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D5⋊AGL(1,𝔽5)
commutatorC2×C52C24×C4
FrattiniC2C23×D5⋊AGL(1,𝔽5)
FittingC22×C4×C52C2×C4
socleC23×C52C22×C4
prime radicalC23×D52C22
cosocleC2×C5⋊D5C25
hypercenterC22×C4D5⋊AGL(1,𝔽5)
hypocenterC52C23×C4⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C23 ◁ C22×C4

5394 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×D4×D5⋊AGL(1,𝔽5)
maximal normal subgroup ofC22×D4×D5⋊AGL(1,𝔽5)
maximal quotient of#72222997

GAP

Past the SmallGroups library coverage — no SmallGroups id.